Quantum Reports doi: 10.3390/quantum5020032

Authors: Richard D. Gill Justo Pastor Lambare

In a sequence of papers, Marian Kupczynski has argued that Bell&rsquo;s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi&rsquo;s concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell&ndash;CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski&rsquo;s claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell&ndash;CHSH inequality is violated, so, despite any other possible imperfections of such experiments, Kupczynski&rsquo;s escape route for local realism is not available.

]]>Quantum Reports doi: 10.3390/quantum5020031

Authors: Vlatko Vedral

In this paper, I would like to outline what I think is the most natural interpretation of quantum mechanics. By natural, I simply mean that it requires the least amount of excess baggage and that it is universal in the sense that it can be consistently applied to all the observed phenomena, including the universe as a whole. I call it the &ldquo;Everything is a Quantum Wave&rdquo; Interpretation (EQWI) because I think this is a more appropriate name than the Many Worlds Interpretation (MWI). The paper explains why this is so.

]]>Quantum Reports doi: 10.3390/quantum5020030

Authors: Saptarshi Chowdhury Neetik Mukherjee Amlan K. Roy

Over the past few decades, confined quantum systems have emerged to be a subject of considerable importance in physical, chemical and biological sciences. Under such stressed conditions, they display many fascinating and notable physical and chemical properties. Here we address this situation by using two plasma models, namely a weakly coupled plasma environment mimicked by a Debye-H&uuml;ckel potential (DHP) and an exponential cosine screened Coulomb potential (ECSCP). On the other hand, the endohedral confinement is achieved via a Woods-Saxon (WS) potential. The critical screening constant, dipole oscillator strength (OS) and polarizability are investigated for an arbitrary state. A Shannon entropy-based strategy has been invoked to study the phase transition here. An increase in Z leads to larger critical screening. Moreover, a detailed investigation reveals that there exists at least one bound state in such plasmas. Pilot calculations are conducted for some low-lying states (&#8467;=1&minus;5) using a generalized pseudo spectral scheme, providing optimal, non-uniform radial discretization.

]]>Quantum Reports doi: 10.3390/quantum5020029

Authors: Ervin K. Lenzi Enrique C. Gabrick Elaheh Sayari Antonio S. M. de Castro José Trobia Antonio M. Batista

We investigate a three-level system in the context of the fractional Schr&ouml;dinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. We first consider the three-level system omitting the kinetic term, i.e., taking into account only the transition among the levels, to analyze the effect of the fractional time derivative. Afterward, we incorporate a kinetic term and the fractional derivative in space to analyze simultaneous wave packet transition and spreading among the levels. For these cases, we obtain analytical and numerical solutions. Our results show a wide variety of behaviors connected to the fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet.

]]>Quantum Reports doi: 10.3390/quantum5020028

Authors: Alessandro Pesci

In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles with the superposed locations, a proposed resolution being graviton emission from quadrupole moments. Here, we focus on the delocalized particle (forgetting about the probe and the gedanken experiment) and explore the conditions (in terms of mass, separation, and recombination time) for graviton emission. Through this, we find that the variations of quadrupole moments in the recombination are generically greatly enhanced if the field is entangled compared to if it is sourced instead by the energy momentum expectation value on the delocalized state (moment variation &sim;md2 in the latter case, with m mass, d separation). In addition, we obtain the (upper) limit recombination time for graviton emission growing as m in place of the naive expectation m. In this, the Planck mass acts as threshold mass (huge, for delocalized objects): no graviton emission is possible below it, however fast the recombination occurs. If this is compared with the decay times foreseen in the collapse models of Di&oacute;si and Penrose (in their basic form), one finds that no (quadrupole) graviton emission from recombination is possible in them. Indeed, right when m becomes large enough to allow for emission, it also becomes too large for the superposition to survive collapse long enough to recombine.

]]>Quantum Reports doi: 10.3390/quantum5020027

Authors: Michael E. Cuffaro Stephan Hartmann

It is argued that those who defend the Everett, or &lsquo;many-worlds&rsquo;, interpretation of quantum mechanics should embrace what we call the general quantum theory of open systems (GT) as the proper framework in which to conduct foundational and philosophical investigations in quantum physics. GT is a wider dynamical framework than its alternative, standard quantum theory (ST). This is true even though GT makes no modifications to the quantum formalism. GT rather takes a different view, what we call the open systems view, of the formalism; i.e., in GT, the dynamics of systems whose physical states are fundamentally represented by density operators are represented as fundamentally open as specified by an in general non-unitary dynamical map. This includes, in principle, the dynamics of the universe as a whole. We argue that the more general dynamics describable in GT can be physically motivated, that there is as much prima facie empirical support for GT as there is for ST, and that GT could be fully in the spirit of the Everett interpretation&mdash;that there might, in short, be little reason for an Everettian not to embrace the more general theoretical landscape that GT allows one to explore.

]]>Quantum Reports doi: 10.3390/quantum5020026

Authors: Dustin Lazarovici

A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett&rsquo;s original account in light of the recent literature on the concept of typicality. It argues that Everett&rsquo;s derivation of the Born rule is sound and, in a certain sense, even an optimal result, and defends it against the charge of circularity. The conclusion is that Everett&rsquo;s typicality argument can successfully ground post-factum explanations of Born statistics, while questions remain about the predictive power of the Many-Worlds interpretation.

]]>Quantum Reports doi: 10.3390/quantum5020025

Authors: Dana Ben Porath Eliahu Cohen

The Leggett&ndash;Garg Inequality (LGI) constrains, under certain fundamental assumptions, the correlations between measurements of a quantity Q at different times. Here, we analyze the LGI and propose similar but somewhat more elaborate inequalities, employing a technique that utilizes the mathematical properties of correlation matrices, which was recently proposed in the context of nonlocal correlations. We also find that this technique can be applied to inequalities that combine correlations between different times (as in LGI) and correlations between different locations (as in Bell inequalities). All the proposed bounds include additional correlations compared to the original ones and also lead to a particular form of complementarity. A possible experimental realization and some applications are briefly discussed.

]]>Quantum Reports doi: 10.3390/quantum5020024

Authors: Jeremy Canfield Anna Galler James K. Freericks

Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schr&ouml;dinger equation for them is solved by using a generalized series solution for the bound states (using the Fr&ouml;benius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schr&ouml;dinger when he solved the wave functions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach to solve all problems whose wave functions are represented in terms of confluent hypergeometric functions, especially for the continuum solutions, which can be determined by an easy-to-program contour integral.

]]>Quantum Reports doi: 10.3390/quantum5020023

Authors: Michael Huber

In this work, an alternative attempt to motivate the Many-Worlds Interpretation (MWI) is undertaken. The usual way of arguing for MWI mostly revolves around how it might solve the measurement problem in a more straightforward and concise manner than rival interpretations. However, here an effort is made to defend MWI in an indirect manner, namely via repeated case discrimination and a process of &lsquo;conceptual elimination&rsquo;. That is, it will be argued that its major rivals, with QBism and Relational Quantum-Mechanics being among the most noteworthy ones, either face conceptual incoherence or conceptually collapse into a variant of MWI. Finally, it is argued that hidden-variable theories face severe challenges when being applied to Quantum Field Theory such that appropriate modifications may lead back to MWI, thereby purportedly leaving MWI as the only viable option.

]]>Quantum Reports doi: 10.3390/quantum5020022

Authors: Pierre A. Deymier Keith Runge M. Arif Hasan Trevor D. Lata Josh A. Levine

We experimentally navigate the Hilbert space of two logical phi-bits supported by an externally driven nonlinear array of coupled acoustic waveguides by parametrically changing the relative phase of the drivers. We observe sharp phase jumps of approximately 180&deg; in the individual phi-bit states as a result of the phase tuning of the drivers. The occurrence of these sharp phase jumps varies from phi-bit to phi-bit. All phi-bit phases also possess a common background dependency on the drivers&rsquo; phase. Within the context of multiple time scale perturbation theory, we develop a simple model of the nonlinear array of externally driven coupled acoustic waveguides to shed light on the possible mechanisms for the experimentally observed behavior of the logical phi-bit phase. Finally, we illustrate the ability to experimentally initialize the state of single- and multiple- phi-bit systems by exploiting the drivers&rsquo; phase as a tuning parameter. We also show that the nonlinear correlation between phi-bits enables parallelism in the manipulation of two- and multi-phi-bit superpositions of states.

]]>Quantum Reports doi: 10.3390/quantum5010021

Authors: Isaac Wilhelm

The centered Everett interpretation solves a problem that various approaches to quantum theory face. In this paper, I continue developing the theory underlying that solution. In particular, I defend the centered Everett interpretation against a few objections, and I provide additional motivation for some of its key features.

]]>Quantum Reports doi: 10.3390/quantum5010020

Authors: José L. Romero Andrei B. Klimov

Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions in a four-dimensional phase-space T&lowast;S2 in the limit of large average angular momentum. The cotangent bundle T&lowast;S2 is also the classical manifold for systems with E(3) symmetry group with appropriately fixed Casimir operators. This allows us to employ the asymptotic form of the star-product proper for variable (integer) spin systems to develop a deformation quantization scheme for a particle moving on the two-dimensional sphere, whose observables are elements of e(3) algebra and the corresponding phase-space is T&lowast;S2. We show that the standard commutation relations of the e(3) algebra are recovered from the corresponding classical Poisson brackets and the explicit expressions for the eigenvalues and eigenfunctions of some quantized classical observables (such as the angular momentum operators and their squares) are obtained.

]]>Quantum Reports doi: 10.3390/quantum5010019

Authors: Oleg V. Mikhailov Denis V. Chachkov

Based on the results of a quantum chemical calculation using the DFT method in the B3PW91/TZVP, OPBE/TZVP, M06/TZVP, and M062/Def2TZVP levels, the possibility of the existence of M(N13) chemical compounds (M = Mn, Fe) that are unknown for these elements has been predicted. Data on the structural parameters, the multiplicity of the ground state, APT and NBO analysis, and standard thermodynamic parameters of formation (standard enthalpy &Delta;fH0, entropy S0, and Gibbs&rsquo;s energy &Delta;fG0) for these compounds are presented.

]]>Quantum Reports doi: 10.3390/quantum5010018

Authors: Hervé Zwirn

I show how the quantum paradoxes occurring when we adopt a standard realist framework (or a framework in which the collapse implies a physical change of the state of the system) vanish if we abandon the idea that a measurement is related (directly or indirectly) to a physical change of state. In Convivial Solipsism, similarly to Everett&rsquo;s interpretation, there is no collapse of the wave function. However, contrary to Everett&rsquo;s interpretation, there is only one world. This also allows us to get rid of any non-locality and to provide a solution to the Wigner&rsquo;s friend problem and its more recent versions.

]]>Quantum Reports doi: 10.3390/quantum5010017

Authors: Michael M. Slepchenkov Pavel V. Barkov Olga E. Glukhova

In this article, quantum methods are used to study the optical properties of composite films formed by AB-stacked bilayer graphene and chiral single-walled carbon nanotubes (SWCNT) (12, 6) with a diameter of 1.2 nm. The analysis of optical properties is carried out on the basis of the results of calculating the diagonal elements of complex optical conductivity tensor in the wavelength range of 0.2&ndash;2 &mu;m. Two cases of electromagnetic radiation polarization are considered: along the X axis (along the graphene bilayer) and along the Y axis (along the nanotube axis). The calculations are performed for three topological models (V1, V2, V3) of composite films, which differ in the width of the graphene bilayer and in the value of the shift between graphene layers. It is found that in the case of polarization along the X axis, the profile of the real part of optical conductivity in the region of extremal and middle UV radiation is determined by SWCNT (12, 6), and in the region of near UV and visible radiations, it is determined by bilayer graphene. In the case of polarization along the Y axis, the profile of the real part of optical conductivity in the region of extremal, near UV, and visible radiation is determined by SWCNT (12, 6), and in the region of the mid-UV range, it is determined by bilayer graphene. Regularities in the change in the profile of the surface optical conductivity of bilayer graphene-SWCNT (12,6) composite films under the action of stretching deformation along the Y axis are revealed. For models V1 (width of the graphene nanoribbon is 0.5 nm, the shift between layers is 0.48 nm) and V2 (width of the graphene nanoribbon is 0.71 nm, the shift between layers is 0.27 nm), the shift of the conductivity peaks in the region of extreme UV radiation along the wavelength to the right is shown. For the model V3 (width of the graphene nanoribbon is 0.92 nm, the shift between layers is 0.06 nm), the shift of the conductivity peaks to the right along the wavelength is observed not only in the region of extreme UV radiation, but also in the region of visible radiation. It is assumed that graphene-SWCNT (12,6) composite films with island topology are promising materials for photodetectors in the UV-visible and near-IR ranges.

]]>Quantum Reports doi: 10.3390/quantum5010016

Authors: Paul Tappenden

The 2022 Tel Aviv conference on the many-worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders&ndash;Wallace&ndash;Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always have a single future. Divergence was explicitly introduced to resolve the problem of pre-measurement uncertainty for Everettian theory, which is universally believed to be absent for fission. Here I maintain that there is indeed pre-measurement uncertainty prior to fission, so long as objective probability is a property of Everettian branches. This is made possible if the universe is a set and branches are subsets with a probability measure. A universe that is a set of universes that are macroscopically isomorphic and span all possible configurations of local be&auml;bles fulfills that role. If objective probability is a property of branches, then a successful Deutsch&ndash;Wallace decision-theoretic argument would justify the Principal Principle and be part of probability theory rather than specific to many-worlds theory. Any macroscopic object in our environment becomes a set of isomorphs with different microscopic configurations, each in an elemental universe (elemental in the set-theoretic sense). This is similar to the many-interacting-worlds theory, but the observer inhabits the set of worlds, not an individual world. An observer has many elemental bodies.

]]>Quantum Reports doi: 10.3390/quantum5010015

Authors: Per Arve

It is shown that the wavefunction describes our observations using the postulate that relates position to the distribution |&Psi;|2. This finding implies that a primary ontology is unnecessary. However, what is real is not directly represented by the wavefunction but by the gauge invariants. In light of the presented ontology, Spacetime State Realism becomes not a fundamental ontology but derived.

]]>Quantum Reports doi: 10.3390/quantum5010014

Authors: David Papineau Thomas Rowe

Everettians generally argue that their view recommends just the same rational choices as orthodoxy. In this note, however, we will show that Everettians should advocate non-standard choices in one specific kind of situation, namely situations where different people have unequal claims to an indivisible good.

]]>Quantum Reports doi: 10.3390/quantum5010013

Authors: Gustavo Álvarez Gorazd Cvetič Bernd A. Kniehl Igor Kondrashuk Ivan Parra-Ferrada

We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with a lower level of supersymmetry, or topological Chern&ndash;Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found using the Cauchy integral formula. The solution restricts the form of the unintegrated gluon distribution as a function of momentum transfer and of Bjorken x. Then, we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behavior in the vicinity of the point x=0 and a smooth behavior in the vicinity of the point x=1.

]]>Quantum Reports doi: 10.3390/quantum5010012

Authors: Tomasz Bigaj

This paper discusses the fundamental assumptions and background of the consistent histories (CH) approach to quantum mechanics. The focus of the paper is on the concept of frameworks. It is proposed that frameworks should be interpreted objectively as observer-independent realities. Two further options are considered: a hidden-variables variant of the CH approach, and a many-worlds version, which considers each individual history belonging to a given family as describing a separate world. The latter interpretation is subsequently compared and contrasted with the standard many-worlds interpretation. Finally, the solution to the measurement problem offered by the many-worlds variant of CH is analyzed and amended.

]]>Quantum Reports doi: 10.3390/quantum5010011

Authors: Mordecai Waegell

In 1948, Schwinger developed a local Lorentz-covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger&rsquo;s theory is presented, which reproduces all of the standard empirical predictions of conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant &ldquo;local hidden variable theory&rdquo; in space-time, whose existence proves definitively that such theories are possible. This does not conflict with Bell&rsquo;s theorem because it is a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems&rsquo; wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given.

]]>Quantum Reports doi: 10.3390/quantum5010010

Authors: Shradha Deshmukh Bikash K. Behera Preeti Mulay

Quantum computing is one of the most promising solutions for solving optimization problems in the healthcare world. Quantum computing development aims to light up the execution of a vast and complex set of algorithmic instructions. For its implementation, the machine learning models are continuously evolving. Hence, the new challenge is to improve the existing complex and critical machine learning training models. Therefore, the healthcare sector is shifting from a classical to a quantum domain to sustain patient-oriented attention to healthcare patrons. This paper presents a hybrid classical-quantum approach for training the unsupervised data models. In order to achieve good performance and optimization of the machine learning algorithms, a quantum k-means (QK-means) clustering problem was deployed on the IBM quantum simulators, i.e.,the IBM QASM simulator. In the first place, the approach was theoretically studied and then implemented to analyze the experimental results. The approach was further tested using small synthetics and cardiovascular datasets on a qsam simulator to obtain the clustering solution. The future direction connecting the dots is the incremental k-means algorithm with the quantum platform, which would open hitherto unimaginable technological doors.

]]>Quantum Reports doi: 10.3390/quantum5010009

Authors: Jesús S. Dehesa

Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information&ndash;theoretical analysis of chemical reactions. This potential will be shown in hydrogenic systems by means of the monotone complexity measures of Cram&eacute;r&ndash;Rao, Fisher&ndash;Shannon and LMC(Lopez-Ruiz, Mancini, Calbet)&ndash;R&eacute;nyi types. These quantities are shown to be analytically determined from first principles, i.e., explicitly in terms of the space dimensionality D, the nuclear charge and the hyperquantum numbers, which characterize the system&rsquo; states. Then, they are applied to several relevant classes of particular states with emphasis on the quasi-spherical and the highly excited Rydberg states, obtaining compact and physically transparent expressions. This is possible because of the use of powerful techniques of approximation theory and orthogonal polynomials, asymptotics and generalized hypergeometric functions.

]]>Quantum Reports doi: 10.3390/quantum5010008

Authors: Ovidiu Cristinel Stoica

We show that the quantum wavefunctional can be seen as a set of classical fields on the 3D space aggregated by a measure. We obtain a complete description of the wavefunctional in terms of classical local beables. With this correspondence, classical explanations of the macro level and of probabilities transfer almost directly to the quantum. A key difference is that, in quantum theory, the classical states coexist in parallel, so the probabilities come from self-location uncertainty. We show that these states are distributed according to the Born rule. The coexistence of classical states implies that there are many worlds, even if we assume the collapse postulate. This leads automatically to a new version of the many-worlds interpretation in which the major objections are addressed naturally. We show that background-free quantum gravity provides additional support for this proposal and suggests why branching happens toward the future.

]]>Quantum Reports doi: 10.3390/quantum5010007

Authors: Valia Allori

In this paper, I argue that the many-worlds theory, even if it is arguably the mathematically most straightforward realist reading of quantum formalism, even if it is arguably local and deterministic, is not universally regarded as the best realist quantum theory because it provides a type of explanation that is not universally accepted. Since people disagree about what desiderata a satisfactory physical theory should possess, they also disagree about which explanatory schema one should look for in a theory, and this leads different people to different options.

]]>Quantum Reports doi: 10.3390/quantum5010006

Authors: Quantum Reports Editorial Office Quantum Reports Editorial Office

High-quality academic publishing is built on rigorous peer review [...]

]]>Quantum Reports doi: 10.3390/quantum5010005

Authors: Michel Boyer Gilles Brassard Nicolas Godbout Rotem Liss Stéphane Virally

Quantum key distribution (QKD) protocols aim at allowing two parties to generate a secret shared key. While many QKD protocols have been proven unconditionally secure in theory, practical security analyses of experimental QKD implementations typically do not take into account all possible loopholes, and practical devices are still not fully characterized for obtaining tight and realistic key rates. We present a simple method of computing secure key rates for any practical implementation of discrete-variable QKD (which can also apply to measurement-device-independent QKD), initially in the single-qubit lossless regime, and we rigorously prove its unconditional security against any possible attack. We hope our method becomes one of the standard tools used for analysing, benchmarking, and standardizing all practical realizations of QKD.

]]>Quantum Reports doi: 10.3390/quantum5010004

Authors: Clement A. Onate Ituen B. Okon Gian. O. Jude Michael C. Onyeaju Akaninyene. D. Antia

The solutions for a combination of the isotropic harmonic oscillator plus the inversely quadratic potentials and a combination of the pseudo-harmonic with inversely quadratic potentials has not been reported, though the individual potentials have been given attention. This study focuses on the solutions of the combination of the potentials, as stated above using the parametric Nikiforov&ndash;Uvarov (PNV) as the traditional technique to obtain the energy equations and their corresponding unnormalized radial wave functions. To deduce the application of these potentials, the expectation values, the uncertainty in the position and momentum, and the thermodynamic properties, such as the mean energy, entropy, heat capacity, and the free mean energy, are also calculated via the partition function. The result shows that the spectra for the PHIQ are higher than the spectra for the IHOIQ. It is also shown that the product of the uncertainties obeyed the Heisenberg uncertainty relation/principle. Finally, the thermal properties of the two potentials exhibit similar behaviours.

]]>Quantum Reports doi: 10.3390/quantum5010003

Authors: Martin Bojowald Artur Tsobanjan

Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of &ldquo;almost-positive&rdquo; states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame&ndash;system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics.

]]>Quantum Reports doi: 10.3390/quantum5010002

Authors: Felipe Castañeda-Ramírez Moisés Martínez-Mares

Scattering matrices that can be diagonalized by a rotation through an angle &theta; in 2&times;2 blocks of independent scattering matrices of rank N, are considered. Assuming that the independent scattering matrices are chosen from one of the circular ensembles, or from the Poisson kernel, the 2N&times;2N scattering matrix may describe the scattering through chaotic cavities with reduced symmetry in the absence, or presence, of direct processes, respectively. To illustrate the effect of such symmetry, the statistical distribution of the dimensionless conductance through a ballistic chaotic cavity in the presence of direct processes is analyzed for N=1 using analytical calculations. We make a conjecture for N=2 in the absence of direct processes, which is verified by numerical random-matrix theory simulations, and the first two moments are calculated analytically for arbitrary N.

]]>Quantum Reports doi: 10.3390/quantum5010001

Authors: Jawad Allam Alex Matzkin

We investigate the effect of time-dependent boundary conditions on the dynamics of a quantum bouncer&mdash;a particle falling in a homogeneous gravitational field on a moving mirror. We examine more particularly the way a moving mirror modifies the properties of the entire wavefunction of a falling particle. We find that some effects, such as the fact that a quantum particle hitting a moving mirror may bounce significantly higher than when the mirror is fixed, are in line with classical intuition. Other effects, such as the change in relative phases or in the current density in spatial regions arbitrarily far from the mirror are specifically quantum. We further discuss how the effects produced by a moving mirror could be observed in link with current experiments, in particular with cold neutrons.

]]>Quantum Reports doi: 10.3390/quantum4040044

Authors: Del Rajan

Distributed Denial-of-Service (DDoS) attacks are a significant issue in classical networks. These attacks have been shown to impact the critical infrastructure of a nation, such as its major financial institutions. The possibility of DDoS attacks has also been identified for quantum networks. In this theoretical work, we introduce a quantum analogue of classical entropic DDoS detection systems and apply it in the context of detecting an attack on a quantum network. In particular, we examine DDoS attacks on a quantum repeater and harness the associated entanglement entropy for the detection system. Our results extend the applicability of quantum information from the domain of data security to the area of network security.

]]>Quantum Reports doi: 10.3390/quantum4040043

Authors: Marta Reboiro Diego Tielas

In this work, we study the thermodynamics of a hybrid system based on the Da Providencia&ndash;Sch&uuml;tte Hamiltonian. The model consists of bosons, i.e., photons in a cavity, interacting with an ensemble of spins through a pseudo-Hermitian Hamiltonian. We compute the exact partition function of the system, and from it, we derive the statistical properties of the system. Finally, we evaluate the work that can be extracted from the system by performing an Otto cycle and discuss the advantages of the proposed pseudo-Hermitian interaction.

]]>Quantum Reports doi: 10.3390/quantum4040042

Authors: Nathaniel Wrobel Anshumitra Baul Ka-Ming Tam Juana Moreno

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding &lsquo;phase&rsquo; of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

]]>Quantum Reports doi: 10.3390/quantum4040041

Authors: Lajos Diósi

Based on the assumption that the standard Schr&ouml;dinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals have survived from the 1980s. The Schr&ouml;dinger&ndash;Newton equation (1984) provides well-localized solitons for free macro-objects but lacks the mechanism of how extended wave functions collapse on solitons. The gravity-related stochastic Schr&ouml;dinger equation (1989) provides the spontaneous collapse, but the resulting solitons undergo a tiny diffusion, leading to an inconvenient steady increase in the kinetic energy. We propose the stochastic Schr&ouml;dinger&ndash;Newton equation, which contains the above two gravity-related modifications together. Then, the wave functions of free macroscopic bodies will gradually and stochastically collapse to solitons, which perform inertial motion without momentum diffusion: conservation of momentum and energy is restored.

]]>Quantum Reports doi: 10.3390/quantum4040040

Authors: Alfredo M. Ozorio de Almeida

Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell of the original Hamiltonian and the other in the energy shell of the driven Hamiltonian, with endpoints that coincide. Viewed in the time domain, the same pair of trajectory segments arises in the semiclassical evaluation of the trace of a compound propagator: the product of the complex exponentials of the original Hamiltonian and of its driven image. It is shown here that the probability density is the double Fourier transform of this trace, and that the closed compound orbits emulate the role played by the periodic orbits in Gutzwiller&rsquo;s trace formula in its semiclassical evaluation. The phase of the oscillations with the energies or the evolution parameters agree with those previously obtained, whereas the amplitude of the contribution of each closed compound orbit is more compact and independent of any feature of the Weyl&ndash;Wigner representation in which the calculation was carried out.

]]>Quantum Reports doi: 10.3390/quantum4040039

Authors: Ademir de J. Santos Frederico V. Prudente Marcilio N. Guimarães Wallas S. Nascimento

We present an informational study of a spherically confined hydrogen atom, a hydrogenic ion confined in a strongly coupled plasma, a spherically confined harmonic oscillator, and a particle confined in a cage. For this, we have implemented a numerical procedure to obtain information entropies of these confined quantum systems. The procedure is based on the variational formalism that uses the finite element method (FEM) for the expansion of the wavefunction in terms of local base functions. Such a study is carried out in order to analyze what happens in the rigorous confinement regime. In particular, we have shown that the effects of the interaction potential is no longer important for rigorous confinements and the studied systems start to behave just like an electron confined by a impenetrable spherical cage. When possible, we compared our results with those published in the literature.

]]>Quantum Reports doi: 10.3390/quantum4040038

Authors: Anatoly Yu. Zakharov

A method is proposed for describing the dynamics of systems of interacting particles in terms of an auxiliary field, which in the static mode is equivalent to given interatomic potentials, and in the dynamic mode is a classical relativistic composite field. It is established that for interatomic potentials, the Fourier transform of which is a rational algebraic function of the wave vector, the auxiliary field is a composition of elementary fields that satisfy the Klein-Gordon equation with complex masses. The interaction between particles carried by the auxiliary field is nonlocal both in space variables and in time. The temporal non-locality is due to the dynamic nature of the auxiliary field and can be described in terms of functional-differential equations of retarded type. Due to the finiteness mass of the auxiliary field, the delay in interactions between particles can be arbitrarily large. A qualitative analysis of the dynamics of few-body and many-body systems with retarded interactions has been carried out, and a non-statistical mechanisms for both the thermodynamic behavior of systems and synergistic effects has been established.

]]>Quantum Reports doi: 10.3390/quantum4040037

Authors: Michel Planat David Chester Marcelo M. Amaral Klee Irwin

We recently proposed that topological quantum computing might be based on SL(2,C) representations of the fundamental group &pi;1(S3\K) for the complement of a link K in the three-sphere. The restriction to links whose associated SL(2,C) character variety V contains a Fricke surface &kappa;d=xyz&minus;x2&minus;y2&minus;z2+d is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link L2a1, one of the three arithmetic two-bridge links (the Whitehead link 512, the Berge link 622 or the double-eight link 632) or the link 732, the V for those links contains the reducible component &kappa;4, the so-called Cayley cubic. In addition, the V for the latter two links contains the irreducible component &kappa;3, or &kappa;2, respectively. Taking &rho; to be a representation with character &kappa;d (d&lt;4), with |x|,|y|,|z|&le;2, then &rho;(&pi;1) fixes a unique point in the hyperbolic space H3 and is a conjugate to a SU(2) representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the four-punctured sphere and Painlev&eacute; VI equation. The 0-surgery on the three circles of the Borromean rings L6a4 is taken as an example.

]]>Quantum Reports doi: 10.3390/quantum4040036

Authors: Miguel Citeli de Freitas Viktor V. Dodonov

In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder&ndash;Glauber&ndash;Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson&ndash;Schr&ouml;dinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered.

]]>Quantum Reports doi: 10.3390/quantum4040035

Authors: Andrey Akhmeteli

The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein&ndash;Gordon&ndash;Maxwell electrodynamics), spinor electrodynamics (Dirac&ndash;Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, and the resulting modified Maxwell equations describe the independent evolution of the electromagnetic field. Similar results were obtained for spinor electrodynamics. Three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and the remaining component can be made real by a gauge transformation. A similar result was obtained for the Dirac equation in the Yang&ndash;Mills field. As quantum gauge theories play a central role in modern physics, the approach of this article may be sufficiently general. One-particle wave functions can be modeled as plasma-like collections of a large number of particles and antiparticles. This seems to enable the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative.

]]>Quantum Reports doi: 10.3390/quantum4040034

Authors: Zoran Rukelj Danko Radić

We report the topological properties, in terms of the Berry phase, of the 2D noninteracting system with electron&ndash;hole band inversion, described by the two-band generalized analogue of the low-energy Bernevig&ndash;Hughes&ndash;Zhang Hamiltonian, yielding the W-shaped energy bands in the form of two intersecting cones with the gap along the closed continuous loop. We identify the range of parameters where the Berry phase attains qualitatively different values: (a) the integer multiplier of 2&pi;, (b) the integer multiplier of &pi;, and (c) the nontrivial value between the latter two, which depends on the system parameters. The system thus exhibits the anomalous quantum Hall effect associated with the nontrivial geometric phase, which is presumably tunable through the choice of parameters at hand.

]]>Quantum Reports doi: 10.3390/quantum4040033

Authors: Agustin Silva Omar Gustavo Zabaleta Constancio Miguel Arizmendi

The quantization of games expand the players strategy space, allowing the emergence of more equilibriums. However, finding these equilibriums is difficult, especially if players are allowed to use mixed strategies. The size of the exploration space expands so much for quantum games that makes far harder to find the player&rsquo;s best strategy. In this work, we propose a method to learn and visualize mixed quantum strategies and compare them with their classical counterpart. In our model, players do not know in advance which game they are playing (pay-off matrix) neither the action selected nor the reward obtained by their competitors at each step, they only learn from an individual feedback reward signal. In addition, we study both the influence of entanglement and noise on the performance of various quantum games.

]]>Quantum Reports doi: 10.3390/quantum4040032

Authors: Pedro Schlottmann

The T=0 excitation spectra of the antiferromagnetic (J&gt;0) anisotropic Heisenberg chain of spins 1/2 are studied using the Bethe Ansatz equations for &Delta;=cos(&pi;/n), n=3,4 and 5. The number of unknown functions is n&minus;1 for &Delta;=cos(&pi;/n) and can be solved numerically for a finite external field. The low-energy excitations form a Luttinger liquid parametrized by a conformal field theory with conformal charge of c=1. For higher energy excitations, the spectral functions display deviations from the Luttinger behavior arising from the curvature in the dispersion. Adding a corrective term of the form of a mobile impurity coupled to the Luttinger liquid modes corrects this difference. The &ldquo;impurity&rdquo; is an irrelevant operator, which if treated non-perturbatively, yields the threshold singularities in the one-spinwave particle and hole Green&rsquo;s function correctly.

]]>Quantum Reports doi: 10.3390/quantum4040031

Authors: Roberto Leporini Davide Pastorello

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination.

]]>Quantum Reports doi: 10.3390/quantum4040030

Authors: Edward Rietman Leslie Schuum Ayush Salik Manor Askenazi Hava Siegelmann

Stephen Wolfram (2002) proposed the concept of computational equivalence, which implies that almost any dynamical system can be considered as a computation, including programmable matter and nonlinear materials such as, so called, quantum matter. Memristors are often used in building and evaluating hardware neural networks. Ukil (2011) demonstrated a theoretical relationship between piezoelectrical materials and memristors. We review that work as a necessary background prior to our work on exploring a piezoelectric material for neural network computation. Our method consisted of using a cubic block of unpoled lead zirconate titanate (PZT) ceramic, to which we have attached wires for programming the PZT as a programmable substrate. We then, by means of pulse trains, constructed on-the-fly internal patterns of regions of aligned polarization and unaligned, or disordered regions. These dynamic patterns come about through constructive and destructive interference and may be exploited as a type of reservoir network. Using MNIST data we demonstrate a learning machine.

]]>Quantum Reports doi: 10.3390/quantum4040029

Authors: Stan Gudder

We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of a single probability measure. We then show that any two probability measures coexist. We extend these concepts to observables and instruments and mention that two observables need not coexist. We define the discretization of an observable as a special case of coarse-graining and show that these have 0&ndash;1 stochastic kernels. We next consider finite observables and instruments and show that in these cases, stochastic kernels are replaced by stochastic matrices. We also show that coarse-graining is the same as post-processing in this finite case. We then consider sequential products of observables and discuss the sequential product of a post-processed observable with another observable. We briefly discuss SIC observables and the example of qubit observables.

]]>Quantum Reports doi: 10.3390/quantum4040028

Authors: Ferenc Márkus Katalin Gambár

Today, two of the most prosperous fields of physics are quantum computing and spintronics. In both, the loss of information and dissipation play a crucial role. In the present work, we formulate the quantization of the dissipative oscillator, which aids the understanding of the abovementioned issues, and creates a theoretical frame to overcome these issues in the future. Based on the Lagrangian framework of the damped spring system, the canonically conjugated pairs and the Hamiltonian of the system are obtained; then, the quantization procedure can be started and consistently applied. As a result, the damping quantum wave equation of the dissipative oscillator is deduced, and an exact damping wave solution of this equation is obtained. Consequently, we arrive at an irreversible quantum theory by which the quantum losses can be described.

]]>Quantum Reports doi: 10.3390/quantum4040027

Authors: Tomah Sogabe Tomoaki Kimura Chih-Chieh Chen Kodai Shiba Nobuhiro Kasahara Masaru Sogabe Katsuyoshi Sakamoto

Artificial intelligence (AI) technology leads to new insights into the manipulation of quantum systems in the Noisy Intermediate-Scale Quantum (NISQ) era. Classical agent-based artificial intelligence algorithms provide a framework for the design or control of quantum systems. Traditional reinforcement learning methods are designed for the Markov Decision Process (MDP) and, hence, have difficulty in dealing with partially observable or quantum observable decision processes. Due to the difficulty of building or inferring a model of a specified quantum system, a model-free-based control approach is more practical and feasible than its counterpart of a model-based approach. In this work, we apply a model-free deep recurrent Q-network (DRQN) reinforcement learning method for qubit-based quantum circuit architecture design problems. This paper is the first attempt to solve the quantum circuit design problem from the recurrent reinforcement learning algorithm, while using discrete policy. Simulation results suggest that our long short-term memory (LSTM)-based DRQN method is able to learn quantum circuits for entangled Bell&ndash;Greenberger&ndash;Horne&ndash;Zeilinger (Bell&ndash;GHZ) states. However, since we also observe unstable learning curves in experiments, suggesting that the DRQN could be a promising method for AI-based quantum circuit design application, more investigation on the stability issue would be required.

]]>Quantum Reports doi: 10.3390/quantum4040026

Authors: Jean-Pierre Gazeau Romain Murenzi

Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to circumvent problems due to the presence of singularities in the classical models. In this paper, we implement covariant integral quantizations for systems whose phase space is Z&times;S1, i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete &amp; compact version of the Weyl&ndash;Heisenberg group, namely the central extension of the abelian group Z&times;SO(2). In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on L2(S1), is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space and resulting resolution of the identity. As particular cases of the latter we recover quantizations with de Bi&egrave;vre-del Olmo&ndash;Gonzales and Kowalski&ndash;Rembielevski&ndash;Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fej&eacute;r kernels. Applications to stellar representations are in progress.

]]>Quantum Reports doi: 10.3390/quantum4030025

Authors: Denis V. Chachkov Oleg V. Mikhailov

By means of the CCSD(T)/6-311++G(df,p) and G4 quantum-chemical calculation methods, the calculation of the molecular and electronic structures of boron&ndash;nitrogen compounds having the B3N3 composition was carried out and its results were discussed. It was noted that seven isomeric forms with different space structures can exist; wherein, the most stable form is a distorted flat hexagon with alternating B and N atoms, with both B and N atoms forming regular triangles, but with different side lengths. The values of geometric parameters of molecular structures in each of these compounds are presented. Also, the key thermodynamic parameters of formation (enthalpy &Delta;fH0, entropy S0, Gibbs&rsquo; energy &Delta;fG0) and relative total energies of these compounds are calculated.

]]>Quantum Reports doi: 10.3390/quantum4030024

Authors: Majid Monajjemi Fatemeh Mollaamin Neda Samiei Soofi

The symmetry breaking (SB) of B2 not only exhibits an energy barrier for ionic or neutral forms dependent on various basis sets but it also exhibits a few SBs due to the asymmetry stretching and bending mode interactions. SB obeys the mechanical quantum theorem among discrete symmetries and their connection to the spin statistics in physical sciences. In this investigation, the unusual amount of energy barrier of SBs appeared upon the orbit&ndash;orbit coupling of BNB (both radical and ions) between transition states and the ground state. Our goal in this study is to understand the difference among the electromagnetic structures of the (B2N(&#8723;,0)) variants due to effects of various basis sets and methods and also the quantum symmetry breaking phenomenon. In the D&infin;h point group of (B2N(&#8723;,0)) variants, the unpaired electron is delocalized, while in the asymmetric C&infin;v point group, it is localized on either one of the B atoms. Structures with broken symmetry, C&infin;v, can be stable by interacting with the D&infin;h point group. In viewpoints of quantum chemistry, the second-order Jahn&ndash;Teller effect permits the unpaired electron to localize on boron atom, rather than being delocalized. In this study, we observed that the energy barrier of SB for BNB increases by post HF methods.

]]>Quantum Reports doi: 10.3390/quantum4030023

Authors: Salim Yasmineh

In Newtonian physics, the equation of motion is invariant when the direction of time (t&rarr;&minus;t) is flipped. However, in quantum physics, flipping the direction of time changes the sign of the Schr&ouml;dinger equation. An anti-unitary operator is needed to restore time reversal in quantum physics, but this is at the cost of not having a consistent definition of time reversal applicable to all fundamental theories. On the other hand, a quantum system&nbsp;composed of a pair of entangled particles behaves in such a manner that when the state of one particle is measured, the second particle &lsquo;simultaneously&rsquo; acquires a determinate state. A notion of absolute simultaneity seems to be inferred by quantum mechanics, even though it is forbidden by the postulates of relativity. We aim to point out that the above two problems can be overcome if the wavefunction is defined with respect to proper time, which in fact is the real physical time instead of ordinary time.

]]>Quantum Reports doi: 10.3390/quantum4030022

Authors: Miloslav Znojil

For the displaced harmonic double-well oscillator, the existence of exact polynomial bound states at certain displacements d is revealed. The N-plets of these quasi-exactly solvable (QES) states are constructed in closed form. For non-QES states, the Schr&ouml;dinger equation can still be considered &ldquo;non-polynomially exactly solvable&rdquo; (NES) because the exact left and right parts of the wave function (proportional to confluent hypergeometric function) just have to be matched in the origin.

]]>Quantum Reports doi: 10.3390/quantum4030021

Authors: Ervin K. Lenzi Luiz R. Evangelista Haroldo V. Ribeiro Richard L. Magin

We investigate the solutions of a two-dimensional Schr&ouml;dinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green&rsquo;s function approach to obtain the solutions, which are given in terms of stretched exponential functions. The results can be linked to the properties of the system and show anomalous spreading for the wave packet. We also analyze the interplay between the backbone structure with branches constraining the different directions and the effective mass. In particular, we show how a fractional Schr&ouml;dinger equation emerges from this scenario.

]]>Quantum Reports doi: 10.3390/quantum4030020

Authors: Fernando Minotti Giovanni Modanese

We reconsider some well-known tunneling processes from the point of view of Aharonov-Bohm electrodynamics, a unique extension of Maxwell&rsquo;s theory which admits charge-current sources that are not locally conserved. In particular we are interested into tunneling phenomena having relatively long range (otherwise the non-Maxwellian effects become irrelevant, especially at high frequency) and involving macroscopic wavefunctions and coherent matter, for which it makes sense to evaluate the classical e.m. field generated by the tunneling particles. For some condensed-matter systems, admitting discontinuities in the probability current is a possible way of formulating phenomenological models. In such cases, the Aharonov-Bohm theory offers a logically consistent approach and allows to derive observable consequences. Typical e.m. signatures of the failure of local conservation are at high frequency the generation of a longitudinal electric radiation field, and at low frequency a small effect of &ldquo;missing&rdquo; magnetic field. Possible causes of this failure are instant tunneling and phase slips in superconductors. For macroscopic quantum systems in which the phase-number uncertainty relation &Delta;N&Delta;&phi;&sim;1 applies, the expectation value of the anomalous source I=&part;t&rho;+&nabla;&middot;j has quantum fluctuations, thus becoming a random source of weak non-Maxwellian fields.

]]>Quantum Reports doi: 10.3390/quantum4030019

Authors: Tuan K. Do Trung V. Phan

Is it possible that two different transitions in the non-relativistic quantum mechanical model of the hydrogen atom give the same frequency of radiation? That is, can different energy level transitions in a hydrogen atom have the same photon radiation frequency? This question, which was asked during a Ph.D. oral exam in 1997 at the University of Colorado Boulder, is well-known among physics graduate students. We show a general solution to this question, in which all equifrequency transition pairs can be obtained from the set of solutions of a Diophantine equation. This fun puzzle is a simple yet concrete example of how number theory can be relevant to quantum systems, a curious theme that emerges in theoretical physics but is usually inaccessible to a general audience.

]]>Quantum Reports doi: 10.3390/quantum4030018

Authors: Lev Vaidman

A brief (subjective) description of the state of the art of the many-worlds interpretation of quantum mechanics (MWI) is presented. It is argued that the MWI is the only interpretation which removes action at a distance and randomness from quantum theory. Limitations of the MWI regarding questions of probability which can be legitimately asked are specified. The ontological picture of the MWI as a theory of the universal wave function decomposed into a superposition of world wave functions, the important parts of which are defined in three-dimensional space, is presented from the point of view of our particular branch. Some speculations about misconceptions, which apparently prevent the MWI from being in the consensus, are mentioned.

]]>Quantum Reports doi: 10.3390/quantum4030017

Authors: Antonio Manzalini Michele Amoretti

A first quantum revolution has already brought quantum technologies into our everyday life for decades: in fact, electronics and optics are based on the quantum mechanical principles. Today, a second quantum revolution is underway, leveraging the quantum principles of superposition, entanglement and measurement, which were not fully exploited yet. International innovation activities and standardization bodies have identified four main application areas for quantum technologies and services: quantum secure communications, quantum computing, quantum simulation, and quantum sensing and metrology. This paper focuses on quantum secure communications by addressing the evolution of Quantum Key Distribution (QKD) networks (under early exploitation today) towards the Quantum-ready networks and the Quantum Internet based also on entanglement distribution. Assuming that management and control of quantum nodes is a key challenge under definition, today, a main obstacle in exploiting long-range QKD and Quantum-ready networks concerns the inherent losses due to the optical transmission channels. Currently, it is assumed that a most promising way for overcoming this limitation, while avoiding the presence of costly trusted nodes, it is to distribute entangled states by means of Quantum Repeaters. In this respect, the paper provides an overview of current methods and systems for end-to-end entanglement generation, with some simulations and a discussion of capacity upper bounds and their impact of secret key rate in QKD systems.

]]>Quantum Reports doi: 10.3390/quantum4030016

Authors: Collins Okon Edet Jonathan E. Osang Norshamsuri Ali Emmanuel Paul Agbo Syed Alwee Aljunid Rosdisham Endut Emmanuel B. Ettah Reza Khordad Akpan Ndem Ikot Muhammad Asjad

In this study, the solutions of the Schrodinger equation (SE) with modified Hylleraas potential in arbitrary dimensions was obtained using the asymptotic iteration method (AIM) to obtain the energy and wave functions, respectively. The energy equation was used to obtain the thermal properties of this system. The effect of the potential parameters and dimensions on the energy spectra and thermal properties was scrutinized thoroughly. It was found that the aforementioned affects the thermal properties and energy spectra, respectively. In addition, we also computed the numerical energy spectra of the MHP for the first time and discussed it in detail. The results of our study can be applied to molecular physics, chemical physics, etc.

]]>Quantum Reports doi: 10.3390/quantum4030015

Authors: Demosthenes Ellinas Christos Konstandakis

Employing the single item search algorithm of N dimensional database it is shown that: First, the entanglement developed between two any-size parts of database space varies periodically during the course of searching. The periodic entanglement of the associated reduced density matrix quantified by several entanglement measures (linear entropy, von Neumann, Renyi), is found to vanish with period O(sqrt(N)). Second, functions of equal entanglement are shown to vary also with equal period. Both those phenomena, based on size-independent database bi-partition, manifest a general scale invariant property of entanglement in quantum search. Third, measuring the entanglement periodicity via the number of searching steps between successive canceling out, determines N, the database set cardinality, quadratically faster than ordinary counting. An operational setting that includes an Entropy observable and its quantum circuits realization is also provided for implementing fast counting. Rigging the marked item initial probability, either by initial advice or by guessing, improves hyper-quadratically the performance of those phenomena.

]]>Quantum Reports doi: 10.3390/quantum4020014

Authors: Graciela Chichilnisky

Based on the axioms of quantum theory, we identify a class of topological singularities that encode a fundamental difference between classic and quantum probability, and explain quantum theory&rsquo;s puzzles and phenomena in simple mathematical terms so they are no longer &lsquo;quantum paradoxes&rsquo;. The singularities provide also new experimental insights and predictions that are presented in this article and establish a surprising new connection between the physical and social sciences. The key is the topology of spaces of quantum events and of the frameworks postulated by these axioms. These are quite different from their counterparts in classic probability and explain mathematically the interference between quantum experiments and the existence of several frameworks or &lsquo;violation of unicity&rsquo; that characterizes quantum physics. They also explain entanglement, the Heisenberg uncertainty principle, order dependence of observations, the conjunction fallacy and geometric phenomena such as Pancharatnam&ndash;Berry phases. Somewhat surprisingly, we find that the same topological singularities explain the impossibility of selecting a social preference among different individual preferences: which is Arrow&rsquo;s social choice paradox: the foundations of social choice and of quantum theory are therefore mathematically equivalent. We identify necessary and sufficient conditions on how to restrict experiments to avoid these singularities and recover unicity, avoiding possible interference between experiments and also quantum paradoxes; the same topological restriction is shown to provide a resolution to the social choice impossibility theorem of Chichilnisky.

]]>Quantum Reports doi: 10.3390/quantum4020013

Authors: Sheng Yi Meijuan Lu Jerome Busemeyer

The psychology of judgment and decision making can provide useful guidance to the task of medical decision making. More specifically, we describe how a new approach to judgment and decisions, based on quantum probability theory, can shed new light on seemingly irrational judgments, as well as indicate ways to ameliorate these judgment errors. Five different types of probability judgment errors that occur in medical decisions are reviewed. For each one, we provide a simple account using theory from quantum cognition. We conclude by drawing the implications of quantum cognition for ameliorating these common medical probability judgment errors.

]]>Quantum Reports doi: 10.3390/quantum4020012

Authors: Sumeet Srinivasa Prasannaa V Bhanu Pratap Das Bijaya Kumar Sahoo

The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous quantum mechanical treatment of the different interactions. In this pilot study, we investigate the physical effects beyond the mean-field approximation, known as electron correlation, in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver algorithm. To this end, we consider three isoelectronic species, namely Be, Li&minus;, and B+. This unique choice spans three classes&mdash;a neutral atom, an anion, and a cation. We have employed the unitary coupled-cluster ans&auml;tz to perform a rigorous analysis of two very important factors that could affect the precision of the simulations of electron correlation effects within a basis, namely mapping and backend simulator. We carry out our all-electron calculations with four such basis sets. The results obtained are compared with those calculated by using the full configuration interaction, traditional coupled-cluster and the unitary coupled-cluster methods, on a classical computer, to assess the precision of our results. A salient feature of the study involves a detailed analysis to find the number of shots (the number of times a variational quantum eigensolver algorithm is repeated to build statistics) required for calculations with IBM Qiskit&rsquo;s QASM simulator backend, which mimics an ideal quantum computer. When more qubits become available, our study will serve as among the first steps taken towards computing other properties of interest to various applications such as new physics beyond the Standard Model of elementary particles and atomic clocks using the variational quantum eigensolver algorithm.

]]>Quantum Reports doi: 10.3390/quantum4020011

Authors: Laura Calvillo Veronica Redaelli Nicola Ludwig Abdallah Barjas Qaswal Alice Ghidoni Andrea Faini Debora Rosa Carolina Lombardi Martino Pengo Patrizia Bossolasco Vincenzo Silani Gianfranco Parati

The recent advances of quantum biology suggest a potential role in biomedical research. Studies related to electromagnetic fields, proton pumping in mitochondrial respiratory chain, quantum theory of T-cell receptor (TCR)-degeneracy, theories on biophotons, pyrophosphates or tubulin as possible carriers for neural information, and quantum properties of ions and protons, might be useful for understanding mechanisms of some serious immune, cardiovascular, and neural pathologies for which classic biomedical research, based on biochemical approach, is struggling to find new therapeutic strategies. A breakthrough in medical knowledge is therefore needed in order to improve the understanding of the complex interactions among various systems and organs typical of such pathologies. In particular, problems related to immune system over-activation, to the role of autonomic nervous system (ANS) dysfunction in the obstructive sleep apnea (OSA) syndrome, to the clinical consequences of ion channels dysfunction and inherited cardiac diseases, could benefit from the new perspective provided by quantum biology advancement. Overall, quantum biology might provide a promising biophysical theoretic system, on which to base pathophysiology understanding and hopefully therapeutic strategies. With the present work, authors hope to open a constructive and multidisciplinary debate on this important topic.

]]>Quantum Reports doi: 10.3390/quantum4020010

Authors: Agustin Silva Omar G. Zabaleta Constancio M. Arizmendi

Because of the sustained growth of information and mobile users transmitting a great amount of data packets, modern network performances are being seriously affected by congestion problems. In fact, congestion management is a challenging task that can be roughly summarized as a trade off between transmission latency and cost. In order to contribute to solve the congestion problem on communication networks, a novel framework based on a quantum game model is proposed, where network packets compete selfishly for their fastest route. Simulations show that final network routing and traveling times achieved with the quantum version outperform those obtained with a classical game model with the same options for packet transmission for both. Pareto optimality and Nash equilibrium are studied as well as the influence of simulated and real noise in the quantum protocol. This leads to the opportunity of developing full-stack protocols that may be capable of taking advantage of the quantum properties for optimizing communication systems. Due to its generality, this game approach can be applied both in classical complex networks and in future quantum networks in order to maximize the performance of the quantum internet.

]]>Quantum Reports doi: 10.3390/quantum4010009

Authors: Diana Monteoliva Angelo Plastino Angel Ricardo Plastino

We deal here with an exactly solvable N-nucleon system that has been used to mimic typical features of quantum many-body systems. There is in the literature some controversy regarding the possible existence of a quantum phase transition in the model. We show here that an appeal to a suitable statistical quantifier called thermal efficiency puts an end to the controversy.

]]>Quantum Reports doi: 10.3390/quantum4010008

Authors: Melanie Swan Renato P. dos Santos Franke Witte

Quantum neurobiology is concerned with potential quantum effects operating in the brain and the application of quantum information science to neuroscience problems, the latter of which is the main focus of the current paper. The human brain is fundamentally a multiscalar problem, with complex behavior spanning nine orders of magnitude-scale tiers from the atomic and cellular level to brain networks and the central nervous system. In this review, we discuss a new generation of bio-inspired quantum technologies in the emerging field of quantum neurobiology and present a novel physics-inspired theory of neural signaling (AdS/Brain (anti-de Sitter space)). Three tiers of quantum information science-directed neurobiology applications can be identified. First are those that interpret empirical data from neural imaging modalities (EEG, MRI, CT, PET scans), protein folding, and genomics with wavefunctions and quantum machine learning. Second are those that develop neural dynamics as a broad approach to quantum neurobiology, consisting of superpositioned data modeling evaluated with quantum probability, neural field theories, filamentary signaling, and quantum nanoscience. Third is neuroscience physics interpretations of foundational physics findings in the context of neurobiology. The benefit of this work is the possibility of an improved understanding of the resolution of neuropathologies such as Alzheimer&rsquo;s disease.

]]>Quantum Reports doi: 10.3390/quantum4010007

Authors: Quantum Reports Editorial Office Quantum Reports Editorial Office

Rigorous peer-reviews are the basis of high-quality academic publishing [...]

]]>Quantum Reports doi: 10.3390/quantum4010006

Authors: Gabriele Agliardi Enrico Prati

Loading data efficiently from classical memories to quantum computers is a key challenge of noisy intermediate-scale quantum computers. Such a problem can be addressed through quantum generative adversarial networks (qGANs), which are noise tolerant and agnostic with respect to data. Tuning a qGAN to balance accuracy and training time is a hard task that becomes paramount when target distributions are multivariate. Thanks to our tuning of the hyper-parameters and of the optimizer, the training of qGAN reduces, on average, the Kolmogorov&ndash;Smirnov statistic of 43&ndash;64% with respect to the state of the art. The ability to reach optima is non-trivially affected by the starting point of the search algorithm. A gap arises between the optimal and sub-optimal training accuracy. We also point out that the simultaneous perturbation stochastic approximation (SPSA) optimizer does not achieve the same accuracy as the Adam optimizer in our conditions, thus calling for new advancements to support the scaling capability of qGANs.

]]>Quantum Reports doi: 10.3390/quantum4010005

Authors: Alistair Victor William Nunn Geoffrey William Guy Jimmy David Bell

Inflammation as a biological concept has been around a long time and derives from the Latin &ldquo;to set on fire&rdquo; and refers to the redness and heat, and usually swelling, which accompanies injury and infection. Chronic inflammation is also associated with ageing and is described by the term &ldquo;inflammaging&rdquo;. Likewise, the biological concept of hormesis, in the guise of what &ldquo;does not kill you, makes you stronger&rdquo;, has long been recognized, but in contrast, seems to have anti-inflammatory and age-slowing characteristics. As both phenomena act to restore homeostasis, they may share some common underlying principles. Thermodynamics describes the relationship between heat and energy, but is also intimately related to quantum mechanics. Life can be viewed as a series of self-renewing dissipative structures existing far from equilibrium as vortexes of &ldquo;negentropy&rdquo; that ages and dies; but, through reproduction and speciation, new robust structures are created, enabling life to adapt and continue in response to ever changing environments. In short, life can be viewed as a natural consequence of thermodynamics to dissipate energy to restore equilibrium; each component of this system is replaceable. However, at the molecular level, there is perhaps a deeper question: is life dependent on, or has it enhanced, quantum effects in space and time beyond those normally expected at the atomistic scale and temperatures that life operates at? There is some evidence it has. Certainly, the dissipative adaptive mechanism described by thermodynamics is now being extended into the quantum realm. Fascinating though this topic is, does exploring the relationship between quantum mechanics, thermodynamics, and biology give us a greater insight into ageing and, thus, medicine? It could be said that hormesis and inflammation are expressions of thermodynamic and quantum principles that control ageing via natural selection that could operate at all scales of life. Inflammation could be viewed as a mechanism to remove inefficient systems in response to stress to enable rebuilding of more functional dissipative structures, and hormesis as the process describing the ability to adapt; underlying this is the manipulation of fundamental quantum principles. Defining what &ldquo;quantum biological normality&rdquo; is has been a long-term problem, but perhaps we do not need to, as it is simply an expression of one end of the normal quantum mechanical spectrum, implying that biology could inform us as to how we can define the quantum world.

]]>Quantum Reports doi: 10.3390/quantum4010004

Authors: Salma Chib Abdelmajid Belafhal

This work examines several analytical evaluations of the Voigt profile, which is a convolution of the Gaussian and Lorentzian profiles, theoretically and numerically. Mathematical derivations are performed concisely to illustrate some closed forms of the considered profile. A representation in terms of special function and a simple and interesting approximation of the Voigt function are well demonstrated, which could have promising applications in several fields of physics, e.g., atmospheric radiative transfer, neutron reactions, molecular spectroscopy, plasma waves, and astrophysical spectroscopy.

]]>Quantum Reports doi: 10.3390/quantum4010003

Authors: Abhinash Kumar Roy Sourabh Magare Varun Srivastava Prasanta K. Panigrahi

We investigate the dynamical evolution of genuine multipartite correlations for N-qubits in a common reservoir considering a non-dissipative qubits-reservoir model. We derive an exact expression for the time-evolved density matrix by modeling the reservoir as a set of infinite harmonic oscillators with a bilinear form of interaction Hamiltonian. Interestingly, we find that the choice of two-level systems corresponding to an initially correlated multipartite state plays a significant role in potential robustness against environmental decoherence. In particular, the generalized W-class Werner state shows robustness against the decoherence for an equivalent set of qubits, whereas a certain generalized GHZ-class Werner state shows robustness for inequivalent sets of qubits. It is shown that the genuine multipartite concurrence (GMC), a measure of multipartite entanglement of an initially correlated multipartite state, experiences an irreversible decay of correlations in the presence of a thermal reservoir. For the GHZ-class Werner state, the region of mixing parameters for which there exists GMC, shrinks with time and with increase in the temperature of the thermal reservoir. Furthermore, we study the dynamical evolution of the relative entropy of coherence and von-Neumann entropy for the W-class Werner state.

]]>Quantum Reports doi: 10.3390/quantum4010002

Authors: Maria Cristina Diamantini Carlo A. Trugenberger Valerii M. Vinokur

We show that the entropy per quantum vortex per layer in superconductors in external magnetic fields is bounded by the universal value kBln2, which explains puzzling results of recent experiments on the Nernst effect.

]]>Quantum Reports doi: 10.3390/quantum4010001

Authors: Halina Grushevskaya George Krylov

Within the earlier developed high-energy-k&rarr;&middot;p&rarr;-Hamiltonian approach to describe graphene-like materials, the simulations of band structure, non-Abelian Zak phases and the complex conductivity of graphene have been performed. The quasi-relativistic graphene model with a number of flavors (gauge fields) NF=3 in two approximations (with and without a pseudo-Majorana mass term) has been utilized as a ground for the simulations. It has been shown that Zak-phases set for the non-Abelian Majorana-like excitations (modes) in graphene represent the cyclic Z12 and this group is deformed into a smaller one Z8 at sufficiently high momenta due to a deconfinement of the modes. Simulations of complex longitudinal low-frequency conductivity have been performed with a focus on effects of spatial dispersion. A spatial periodic polarization in the graphene models with the pseudo Majorana charge carriers is offered.

]]>Quantum Reports doi: 10.3390/quantum3040047

Authors: Gulnara Abd-Rashidovna Yuldasheva Assel Kurmanaliyeva Aleksandr Ilin

Chromatographic analysis shows that the ionic nanostructured complex of the FS-1 drug contains nanocomplexes of &alpha;-dextrin with a size of ~40&ndash;48 &Aring;. Based on good agreement between the UV spectra of the model structures and the experimental spectrum of the FS-1 drug, the structure of the active FS-1 nanocomplex is proposed. The structure of the active centers of the drug in the dextrin ring was calculated using the quantum-chemical approach DFT/B3PW91. The active centers, i.e., a complex of molecular iodine with lithium halide (I), a binuclear complex of magnesium and lithium containing molecular iodine, triiodide (II), and triiodide (III), are located inside the dextrin helix. The polypeptide outside the dextrin helix forms a hydrogen bond with dextrin in Complex I and coordinates the molecular iodine in Complex II. It is revealed that the active centers of the FS-1drug can be segregated from the dextrin helix and form complexes with DNA nucleotide triplets. The active centers of the FS-1 drug are only segregated on specific sections of DNA. The formation of a complex between the DNA nucleotide and the active center of FS-1 is a key stage in the mechanisms of anti-HIV, anti-coronavirus (Complex I) and antibacterial action (Complex II).

]]>Quantum Reports doi: 10.3390/quantum3040046

Authors: Norio Inui

The Casimir effect between type-II superconducting plates in the coexisting phase of a superconducting phase and a normal phase is investigated. The dependence of the optical conductivity of the superconducting plates on the external magnetic field is described in terms of the penetration depth of the incident electromagnetic field, and the permittivity along the imaginary axis is represented by a linear combination of the permittivities for the plasma model and Drude models. The characteristic frequency in each model is determined using the force parameters for the motion of the magnetic field vortices. The Casimir force between parallel YBCO plates in the mixed state is calculated, and the dependence on the applied magnetic field and temperature is considered.

]]>Quantum Reports doi: 10.3390/quantum3040045

Authors: Anatoly Yu. Zakharov Maxim A. Zakharov

The dynamics of free and forced vibrations of a chain of particles are investigated in a harmonic model taking into account the retardation of interactions between atoms. It is found that the retardation of interactions between particles leads to the non-existence of stationary free vibrations of the crystal lattice. It is shown that in the case of a stable lattice, forced vibrations, regardless of the initial conditions, pass into a stationary regime. A non-statistical dynamic mechanism of the irreversible thermodynamic equilibration is proposed.

]]>Quantum Reports doi: 10.3390/quantum3040044

Authors: Fernando Minotti Giovanni Modanese

In quantum theory, for a system with macroscopic wavefunction, the charge density and current density are represented by non-commuting operators. It follows that the anomaly I=∂tρ+∇·j, being essentially a linear combination of these two operators in the frequency-momentum domain, does not admit eigenstates and has a minimum uncertainty fixed by the Heisenberg relation ΔNΔϕ≃1, which involves the occupation number and the phase of the wavefunction. We give an estimate of the minimum uncertainty in the case of a tunnel Josephson junction made of Nb. Due to this violation of the local conservation of charge, for the evaluation of the e.m. field generated by the system it is necessary to use the extended Aharonov–Bohm electrodynamics. After recalling its field equations, we compute in general form the energy–momentum tensor and the radiation power flux generated by a localized oscillating source. The physical requirements that the total flux be positive, negative or zero yield some conditions on the dipole moment of the anomaly I.

]]>Quantum Reports doi: 10.3390/quantum3040043

Authors: Radouan Hab-arrih Ahmed Jellal Dionisis Stefanatos Abdeldjalil Merdaci

In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.

]]>Quantum Reports doi: 10.3390/quantum3040042

Authors: Hans Cruz-Prado Alessandro Bravetti Angel Garcia-Chung

Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation by using appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems for which it is shown, by means of the corresponding contact master equation, that the resulting dynamics constitute a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes.

]]>Quantum Reports doi: 10.3390/quantum3040041

Authors: Vikram Athalye Emmanuel Haven

Since the beginning of the 21st century, a new interdisciplinary research movement has started, which aims at developing quantum math-like (or simply quantum-like) models to provide an explanation for a variety of socio-economic processes and human behaviour. By making use of mainly the probabilistic aspects of quantum theory, this research movement has led to many important results in the areas of decision-making and finance. In this article, we introduce a novel and more exhaustive approach, to analyze the socio-economic processes and activities, than the pure quantum math-like modelling approach, by taking into account the physical foundations of quantum theory. We also provide a plausibility argument for its exhaustiveness in terms of what we can expect from such an approach, when it is applied to, for example, a generic socio-economic decision process.

]]>Quantum Reports doi: 10.3390/quantum3040040

Authors: Louis Narens

In 1933, Kolmogorov synthesized the basic concepts of probability that were in general use at the time into concepts and deductions from a simple set of axioms that said probability was a σ-additive function from a boolean algebra of events into [0, 1]. In 1932, von Neumann realized that the use of probability in quantum mechanics required a different concept that he formulated as a σ-additive function from the closed subspaces of a Hilbert space onto [0,1]. In 1935, Birkhoff &amp; von Neumann replaced Hilbert space with an algebraic generalization. Today, a slight modification of the Birkhoff-von Neumann generalization is called “quantum logic”. A central problem in the philosophy of probability is the justification of the definition of probability used in a given application. This is usually done by arguing for the rationality of that approach to the situation under consideration. A version of the Dutch book argument given by de Finetti in 1972 is often used to justify the Kolmogorov theory, especially in scientific applications. As von Neumann in 1955 noted, and his criticisms still hold, there is no acceptable foundation for quantum logic. While it is not argued here that a rational approach has been carried out for quantum physics, it is argued that (1) for many important situations found in behavioral science that quantum probability theory is a reasonable choice, and (2) that it has an arguably rational foundation to certain areas of behavioral science, for example, the behavioral paradigm of Between Subjects experiments.

]]>Quantum Reports doi: 10.3390/quantum3040039

Authors: Morteza Sasani Ghamsari

Integration of chip-scale quantum technology was the main aim of this study. First, the recent progress on silicon-based photonic integrated circuits is surveyed, and then it is shown that silicon integrated quantum photonics can be considered a compelling platform for the future of quantum technologies. Among subsections of quantum technology, quantum emitters were selected as the object, and different quantum emitters such as quantum dots, 2D materials, and carbon nanotubes are introduced. Later on, the most recent progress is highlighted to provide an extensive overview of the development of chip-scale quantum emitters. It seems that the next step towards the practical application of quantum emitters is to generate position-controlled quantum light sources. Among developed processes, it can be recognized that droplet–epitaxial QD growth has a promising future for the preparation of chip-scale quantum emitters.

]]>Quantum Reports doi: 10.3390/quantum3040038

Authors: William Sulis

Contextuality is often described as a unique feature of the quantum realm, which distinguishes it fundamentally from the classical realm. This is not strictly true, and stems from decades of the misapplication of Kolmogorov probability. Contextuality appears in Kolmogorov theory (observed in the inability to form joint distributions) and in non-Kolmogorov theory (observed in the violation of inequalities of correlations). Both forms of contextuality have been observed in psychological experiments, although the first form has been known for decades but mostly ignored. The complex dynamics of neural systems (neurobehavioural regulatory systems) and of collective intelligence systems (social insect colonies) are described. These systems are contextual in the first sense and possibly in the second as well. Process algebra, based on the Process Theory of Whitehead, describes systems that are generated, transient, open, interactive, and primarily information-driven, and seems ideally suited to modeling these systems. It is argued that these dynamical characteristics give rise to contextuality and non-Kolmogorov probability in spite of these being entirely classical systems.

]]>Quantum Reports doi: 10.3390/quantum3030037

Authors: Paola Zizzi

In this paper, we demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogolyubov transformations lead to pairs of the spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

]]>Quantum Reports doi: 10.3390/quantum3030036

Authors: Thomas Scheidsteger Robin Haunschild Lutz Bornmann Christoph Ettl

The second quantum technological revolution started around 1980 with the control of single quantum particles and their interaction on an individual basis. These experimental achievements enabled physicists, engineers, and computer scientists to utilize long-known quantum features—especially superposition and entanglement of single quantum states—for a whole range of practical applications. We use a publication set of 54,598 papers from Web of Science, published between 1980 and 2018, to investigate the time development of four main subfields of quantum technology in terms of numbers and shares of publications, as well as the occurrence of topics and their relation to the 25 top contributing countries. Three successive time periods are distinguished in the analyses by their short doubling times in relation to the whole Web of Science. The periods can be characterized by the publication of pioneering works, the exploration of research topics, and the maturing of quantum technology, respectively. Compared to the USA, China’s contribution to the worldwide publication output is overproportionate, but not in the segment of highly cited papers.

]]>Quantum Reports doi: 10.3390/quantum3030035

Authors: Ivan Horváth

Indeterminacy associated with the probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here, we express it as an effective amount (measure) of distinct outcomes instead. The resulting μ-uncertainties are described by the effective number theory whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive μ-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the μ-entropies, convey how many degrees of freedom are effectively involved in a given measurement process. In order to construct quantum μ-entropies, we are led to quantum effective numbers designed to count independent, mutually orthogonal states effectively comprising a density matrix. This concept is basis-independent and leads to a measure-based characterization of entanglement.

]]>Quantum Reports doi: 10.3390/quantum3030034

Authors: Miloslav Znojil

It is well known that, using the conventional non-Hermitian but PT−symmetric Bose–Hubbard Hamiltonian with real spectrum, one can realize the Bose–Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit, characterized by a minimal geometric multiplicity K&nbsp;=&nbsp;1. In our paper, we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose–Hubbard model, which remains exactly solvable while admitting any value of K≥1. It offers a complete menu of benchmark models numbered by a specific combinatorial scheme. In this manner, an exhaustive classification of the general BEC patterns with any geometric multiplicity is obtained and realized in terms of an exactly solvable generalized Bose–Hubbard model.

]]>Quantum Reports doi: 10.3390/quantum3030033

Authors: Oscar Rosas-Ortiz Kevin Zelaya

Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode SU(2) coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation.

]]>Quantum Reports doi: 10.3390/quantum3030032

Authors: Roberto Leporini Davide Pastorello

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification.

]]>Quantum Reports doi: 10.3390/quantum3030031

Authors: Charlyne de Gosson Maurice de Gosson

It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of quantum states for which this property is satisfied; these states are dubbed “Feichtinger states” because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980s by H. Feichtinger. The properties of these states were studied, giving us the opportunity to prove an extension to the general case of a result due to Jaynes on the non-uniqueness of the statistical ensemble, generating a density operator.

]]>Quantum Reports doi: 10.3390/quantum3030030

Authors: Kevin Zelaya Oscar Rosas-Ortiz

We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectra, and transit to the Hermitian configuration for the appropriate values of the involved parameters. We provide a concrete generalization of the Swanson oscillator that includes the Caldirola–Kanai model as a particular case. Explicit solutions are given in both the classical and quantum pictures.

]]>Quantum Reports doi: 10.3390/quantum3030029

Authors: Carlo Cafaro Paul M. Alsing

We present a simple proof of the fact that the minimum time TAB for quantum evolution between two arbitrary states A and B equals TAB=ℏcos−1A|B/ΔE with ΔE being the constant energy uncertainty of the system. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure ε of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the inequality ε≤1 even when the system only passes through nonorthogonal quantum states.

]]>Quantum Reports doi: 10.3390/quantum3030028

Authors: Golriz Hoseinimanesh Naser Mohammadzadeh

The physical synthesis concept for quantum circuits, the interaction between synthesis and physical design processes, was first introduced in our previous work. This concept inspires us to propose some techniques that can minimize the number of extra inserted SWAP operations required to run a circuit on a nearest-neighbor architecture. Minimizing the number of SWAP operations potentially decreases the latency and error probability of a quantum circuit. Focusing on this concept, we present a physical synthesis technique based on transformation rules to decrease the number of SWAP operations in nearest-neighbor architectures. After the qubits of a circuit are mapped onto the physical qubits provided by the target architecture, our procedure is fed by this mapping information. Our method uses the obtained placement and scheduling information to apply some transformation rules to the original netlist to decrease the number of extra SWAP gates required for running the circuit on the architecture. We follow two policies in applying a transformation rule, greedy and simulated-annealing-based policies. Simulation results show that the proposed technique decreases the average number of extra SWAP operations by about 20.6% and 24.1% based on greedy and simulated-annealing-based policies, respectively, compared with the best in the literature.

]]>Quantum Reports doi: 10.3390/quantum3030027

Authors: Jonathan Friedman Lev Mourokh Michele Vittadello

We propose a physical mechanism of conformation-induced proton pumping in mitochondrial Complex I. The structural conformations of this protein are modeled as the motion of a piston having positive charges on both sides. A negatively charged electron attracts the piston, moving the other end away from the proton site, thereby reducing its energy and allowing a proton to populate the site. When the electron escapes, elastic forces assist the return of the piston, increasing proton site energy and facilitating proton transfer. We derive the Heisenberg equations of motion for electron and proton operators and rewrite them in the form of rate equations coupled to the phenomenological Langevin equation describing piston dynamics. This set of coupled equations is solved numerically. We show that proton pumping can be achieved within this model for a reasonable set of parameters. The dependencies of proton current on geometry, temperature, and other parameters are examined.

]]>Quantum Reports doi: 10.3390/quantum3030026

Authors: Sarang S. Bhosale Biswanath Rath Prasanta K. Panigrahi

Bell’s inequality is investigated in parity-time (PT) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone, with two PT-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with CPT inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in PT-symmetric quantum theory is preserved.

]]>Quantum Reports doi: 10.3390/quantum3030025

Authors: Federico Holik César Massri Angelo Plastino Manuel Sáenz

We discuss different formal frameworks for the description of generalized probabilities in statistical theories. We analyze the particular cases of probabilities appearing in classical and quantum mechanics and the approach to generalized probabilities based on convex sets. We argue for considering quantum probabilities as the natural probabilistic assignments for rational agents dealing with contextual probabilistic models. In this way, the formal structure of quantum probabilities as a non-Boolean probabilistic calculus is endowed with a natural interpretation.

]]>Quantum Reports doi: 10.3390/quantum3030024

Authors: Francisco J. Sevilla Andrea Valdés-Hernández Alan J. Barrios

We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between τ and the energy spectrum and allowing the classification of {ri} into families organized in a 2-simplex, δ2. Furthermore, the states determined by {ri} are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those ris in δ2 correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

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