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Quantum Rep., Volume 5, Issue 2 (June 2023) – 13 articles

Cover Story (view full-size image): We investigated a three-level system in the context of the fractional Schrödinger equation by considering fractional differential operators in time and space, which promote anomalous relaxations and spreading of the wave packet. Our results show a wide variety of behaviors connected to fractional operators, such as the non-conservation of probability and the anomalous spread of the wave packet. View this paper
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16 pages, 430 KiB  
Article
Teleportation Revealed
by Charles Alexandre Bédard
Quantum Rep. 2023, 5(2), 510-525; https://doi.org/10.3390/quantum5020034 - 13 Jun 2023
Viewed by 2090
Abstract
Quantum teleportation is the name of a problem: How can the real-valued parameters encoding the state at Alice’s location make their way to Bob’s location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a [...] Read more.
Quantum teleportation is the name of a problem: How can the real-valued parameters encoding the state at Alice’s location make their way to Bob’s location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick. Investigating the phenomenon with Schrödinger states and reduced density matrices shall always leave loose ends because they are not local and complete descriptions of quantum systems. Upon demonstrating that the Heisenberg picture admits a local and complete description, Deutsch and Hayden rendered its explanatory power manifest by revealing the trick behind teleportation, namely, by providing an entirely local account. Their analysis is re-exposed and further developed. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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14 pages, 561 KiB  
Article
Quantum Probability from Temporal Structure
by Michael Ridley
Quantum Rep. 2023, 5(2), 496-509; https://doi.org/10.3390/quantum5020033 - 12 Jun 2023
Viewed by 2243
Abstract
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In ψ-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified using fractions of a [...] Read more.
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In ψ-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified using fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schrödinger dynamics, with a network of ‘fixed points’ defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre- and postselection. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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15 pages, 1148 KiB  
Article
Kupczynski’s Contextual Locally Causal Probabilistic Models Are Constrained by Bell’s Theorem
by Richard D. Gill and Justo Pastor Lambare
Quantum Rep. 2023, 5(2), 481-495; https://doi.org/10.3390/quantum5020032 - 06 Jun 2023
Cited by 1 | Viewed by 1245
Abstract
In a sequence of papers, Marian Kupczynski has argued that Bell’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’s concept of a contextual locally [...] Read more.
In a sequence of papers, Marian Kupczynski has argued that Bell’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’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–CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski’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–CHSH inequality is violated, so, despite any other possible imperfections of such experiments, Kupczynski’s escape route for local realism is not available. Full article
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6 pages, 235 KiB  
Opinion
The Everything-Is-a-Quantum-Wave Interpretation of Quantum Physics
by Vlatko Vedral
Quantum Rep. 2023, 5(2), 475-480; https://doi.org/10.3390/quantum5020031 - 06 Jun 2023
Viewed by 2976
Abstract
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 [...] Read more.
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 “Everything is a Quantum Wave” Interpretation (EQWI) because I think this is a more appropriate name than the Many Worlds Interpretation (MWI). The paper explains why this is so. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
16 pages, 747 KiB  
Article
Hydrogen-like Plasmas under Endohedral Cavity
by Saptarshi Chowdhury, Neetik Mukherjee and Amlan K. Roy
Quantum Rep. 2023, 5(2), 459-474; https://doi.org/10.3390/quantum5020030 - 30 May 2023
Cited by 3 | Viewed by 1297
Abstract
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 [...] Read more.
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-Hückel 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 (=15) using a generalized pseudo spectral scheme, providing optimal, non-uniform radial discretization. Full article
(This article belongs to the Topic Theoretical, Quantum and Computational Chemistry)
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17 pages, 1728 KiB  
Article
Anomalous Relaxation and Three-Level System: A Fractional Schrödinger Equation Approach
by Ervin K. Lenzi, Enrique C. Gabrick, Elaheh Sayari, Antonio S. M. de Castro, José Trobia and Antonio M. Batista
Quantum Rep. 2023, 5(2), 442-458; https://doi.org/10.3390/quantum5020029 - 26 May 2023
Cited by 1 | Viewed by 1801
Abstract
We investigate a three-level system in the context of the fractional Schrödinger 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., [...] Read more.
We investigate a three-level system in the context of the fractional Schrödinger 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. Full article
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16 pages, 388 KiB  
Article
Conditions for Graviton Emission in the Recombination of a Delocalized Mass
by Alessandro Pesci
Quantum Rep. 2023, 5(2), 426-441; https://doi.org/10.3390/quantum5020028 - 22 May 2023
Cited by 2 | Viewed by 1230
Abstract
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 [...] Read more.
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 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 Diósi 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. Full article
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8 pages, 276 KiB  
Article
The Open Systems View and the Everett Interpretation
by Michael E. Cuffaro and Stephan Hartmann
Quantum Rep. 2023, 5(2), 418-425; https://doi.org/10.3390/quantum5020027 - 28 Apr 2023
Viewed by 2091
Abstract
It is argued that those who defend the Everett, or ‘many-worlds’, 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. [...] Read more.
It is argued that those who defend the Everett, or ‘many-worlds’, 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—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. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
11 pages, 471 KiB  
Article
How Everett Solved the Probability Problem in Everettian Quantum Mechanics
by Dustin Lazarovici
Quantum Rep. 2023, 5(2), 407-417; https://doi.org/10.3390/quantum5020026 - 26 Apr 2023
Viewed by 1839
Abstract
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’s original account in light of the recent literature on [...] Read more.
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’s original account in light of the recent literature on the concept of typicality. It argues that Everett’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’s typicality argument can successfully ground post-factum explanations of Born statistics, while questions remain about the predictive power of the Many-Worlds interpretation. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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9 pages, 620 KiB  
Article
Leggett–Garg-like Inequalities from a Correlation Matrix Construction
by Dana Ben Porath and Eliahu Cohen
Quantum Rep. 2023, 5(2), 398-406; https://doi.org/10.3390/quantum5020025 - 23 Apr 2023
Viewed by 1367
Abstract
The Leggett–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 [...] Read more.
The Leggett–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. Full article
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28 pages, 657 KiB  
Article
The Laplace Method for Energy Eigenvalue Problems in Quantum Mechanics
by Jeremy Canfield, Anna Galler and James K. Freericks
Quantum Rep. 2023, 5(2), 370-397; https://doi.org/10.3390/quantum5020024 - 20 Apr 2023
Cited by 1 | Viewed by 1752
Abstract
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present). [...] Read more.
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius 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 Schrödinger 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. Full article
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25 pages, 396 KiB  
Review
Defending Many Worlds via Case Discrimination: An Attempt to Showcase the Conceptual Incoherence of Anti-Realist Interpretations and Relational Quantum Mechanics
by Michael Huber
Quantum Rep. 2023, 5(2), 345-369; https://doi.org/10.3390/quantum5020023 - 18 Apr 2023
Cited by 1 | Viewed by 1566
Abstract
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 [...] Read more.
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 ‘conceptual elimination’. 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. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
20 pages, 3637 KiB  
Article
Tuning Logical Phi-Bit State Vectors in an Externally Driven Nonlinear Array of Acoustic Waveguides via Drivers’ Phase
by Pierre A. Deymier, Keith Runge, M. Arif Hasan, Trevor D. Lata and Josh A. Levine
Quantum Rep. 2023, 5(2), 325-344; https://doi.org/10.3390/quantum5020022 - 06 Apr 2023
Cited by 2 | Viewed by 1311
Abstract
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° in the individual phi-bit states [...] Read more.
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° 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’ 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’ 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. Full article
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