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Quantum Probability and Randomness IV
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Quantum Probability and Randomness IV

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (1 June 2023) | Viewed by 17708

Special Issue Editors

Prof. Dr. Andrei Khrennikov

E-Mail Website
Guest Editor
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden
Interests: quantum foundations; information; probability; contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, and social and political sciences; p-adic numbers; p-adic and ultrametric analysis; dynamical systems; p-adic theoretical physics; utrametric models of cognition and psychological behavior; p-adic models in geophysics and petroleum research
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Karl Svozil

E-Mail Website
Guest Editor
Institute for Theoretical Physics, Vienna University of Technology Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria
Interests: quantum logic; automaton logic; conventionality in relativity theory; intrinsic embedded observers; physical (in)determinism; physical random number generators; generalized probability theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This is the fourth Special Issue devoted to the theme of “Quantum Probability and Randomness”; for the first three issues, see:

https://www.mdpi.com/si/entropy/Probability_Randomness

https://www.mdpi.com/si/entropy/Probability_Randomness_ii

https://www.mdpi.com/journal/entropy/special_issues/Probability_Randomness_iii

The previous Special Issues collected a sample of high-quality papers, both theoretical and experiment-related, written by experts in this area, which attracted considerable interest (including numerous downloads). This is why we have decided to proceed once again with this hot topic by considering structuring this theme into a regular series based on the Entropy journal.

The last few years have been characterized by tremendous developments in quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. Despite the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness.

Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meanings of its basic tools, starting with the Born rule, are among the topics which will be covered in this Special Issue.

Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, the quantum probabilistic treatment of problems of the theory of decision-making under uncertainty. Such studies are also among the topics addressed in this Special Issue. 

The areas covered include:

  • Foundations of quantum information theory and quantum probability;
  • Quantum versus classical randomness and quantum random generators;
  • Generalized probabilistic models;
  • Quantum contextuality and generalized contextual models;
  • Bell’s inequality, entanglement, and randomness;
  • Quantum-like probabilistic modeling of the process of decision making under uncertainty;
  • Quantum probability and information in biology.

Of course, possible topics need not be restricted to the list above; any contribution directed to the improvement of quantum foundations, and the development of quantum probability and randomness is welcome.

Prof. Dr. Andrei Khrennikov
Prof. Dr. Karl Svozil
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum foundation
  • quantum vs. classical probability and randomness
  • quantum information
  • Bell inequality
  • entanglement
  • contextuality
  • random generators
  • generalized probabilistic models

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Published Papers (15 papers)

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Research

17 pages, 332 KiB  
Article
Probability Distributions Describing Qubit-State Superpositions
by Margarita A. Man’ko and Vladimir I. Man’ko
Entropy 2023, 25(10), 1366; https://doi.org/10.3390/e25101366 - 22 Sep 2023
Viewed by 721
Abstract
We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated [...] Read more.
We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
44 pages, 1461 KiB  
Article
Systems of Precision: Coherent Probabilities on Pre-Dynkin Systems and Coherent Previsions on Linear Subspaces
by Rabanus Derr and Robert C. Williamson
Entropy 2023, 25(9), 1283; https://doi.org/10.3390/e25091283 - 31 Aug 2023
Cited by 1 | Viewed by 827
Abstract
In the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision of a [...] Read more.
In the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision of a lower and upper probability form a so-called (pre-)Dynkin system. Interestingly, there are several settings, ranging from machine learning on partial data over frequential probability theory to quantum probability theory and decision making under uncertainty, in which, a priori, the probabilities are only desired to be precise on a specific underlying set system. Here, (pre-)Dynkin systems have been adopted as systems of precision, too. We show that, under extendability conditions, those pre-Dynkin systems equipped with probabilities can be embedded into algebras of sets. Surprisingly, the extendability conditions elaborated in a strand of work in quantum probability are equivalent to coherence from the imprecise probability literature. On this basis, we spell out a lattice duality which relates systems of precision to credal sets of probabilities. We conclude the presentation with a generalization of the framework to expectation-type counterparts of imprecise probabilities. The analogue of pre-Dynkin systems turns out to be (sets of) linear subspaces in the space of bounded, real-valued functions. We introduce partial expectations, natural generalizations of probabilities defined on pre-Dynkin systems. Again, coherence and extendability are equivalent. A related but more general lattice duality preserves the relation between systems of precision and credal sets of probabilities. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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57 pages, 732 KiB  
Article
Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups
by Christopher S. Jackson and Carlton M. Caves
Entropy 2023, 25(9), 1254; https://doi.org/10.3390/e25091254 - 23 Aug 2023
Cited by 2 | Viewed by 1078
Abstract
We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations [...] Read more.
We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument’s evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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17 pages, 359 KiB  
Article
Joint Probabilities Approach to Quantum Games with Noise
by Alexis R. Legón and Ernesto Medina
Entropy 2023, 25(8), 1222; https://doi.org/10.3390/e25081222 - 16 Aug 2023
Viewed by 849
Abstract
A joint probability formalism for quantum games with noise is proposed, inspired by the formalism of non-factorizable probabilities that connects the joint probabilities to quantum games with noise. Using this connection, we show that the joint probabilities are non-factorizable; thus, noise does not [...] Read more.
A joint probability formalism for quantum games with noise is proposed, inspired by the formalism of non-factorizable probabilities that connects the joint probabilities to quantum games with noise. Using this connection, we show that the joint probabilities are non-factorizable; thus, noise does not generically destroy entanglement. This formalism was applied to the Prisoner’s Dilemma, the Chicken Game, and the Battle of the Sexes, where noise is coupled through a single parameter μ. We find that for all the games except for the Battle of the Sexes, the Nash inequalities are maintained up to a threshold value of the noise. Beyond the threshold value, the inequalities no longer hold for quantum and classical strategies. For the Battle of the sexes, the Nash inequalities always hold, no matter the noise strength. This is due to the symmetry and anti-symmetry of the parameters that determine the joint probabilities for that game. Finally, we propose a new correlation measure for the games with classical and quantum strategies, where we obtain that the incorporation of noise, when we have quantum strategies, does not affect entanglement, but classical strategies result in behavior that approximates quantum games with quantum strategies without the need to saturate the system with the maximum value of noise. In this manner, these correlations can be understood as entanglement for our game approach. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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57 pages, 592 KiB  
Article
Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group
by Christopher S. Jackson and Carlton M. Caves
Entropy 2023, 25(8), 1221; https://doi.org/10.3390/e25081221 - 16 Aug 2023
Cited by 2 | Viewed by 865
Abstract
The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the [...] Read more.
The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
24 pages, 456 KiB  
Article
A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems
by Igor G. Vladimirov
Entropy 2023, 25(8), 1179; https://doi.org/10.3390/e25081179 - 08 Aug 2023
Viewed by 571
Abstract
This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson–Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system–field [...] Read more.
This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson–Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system–field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system–field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. As performance criteria, such settings employ quadratic (or more complicated) cost functionals of the system and field variables to be minimized over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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0 pages, 1029 KiB  
Article
Non-Kochen–Specker Contextuality
by Mladen Pavičić
Entropy 2023, 25(8), 1117; https://doi.org/10.3390/e25081117 - 26 Jul 2023
Cited by 1 | Viewed by 1405 | Correction
Abstract
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen–Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and [...] Read more.
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen–Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods—whose complexity does not scale up with the dimension—for generating such non-Kochen–Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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11 pages, 295 KiB  
Article
Gas of Particles Obeying the Monotone Statistics
by Francesco Fidaleo
Entropy 2023, 25(7), 1095; https://doi.org/10.3390/e25071095 - 21 Jul 2023
Viewed by 704
Abstract
The present note is devoted to the detailed investigation of a concrete model satisfying the block-monotone statistics introduced in a previous paper (joint, with collaborators) of the author. The model under consideration indeed describes the free gas of massless particles in a one-dimensional [...] Read more.
The present note is devoted to the detailed investigation of a concrete model satisfying the block-monotone statistics introduced in a previous paper (joint, with collaborators) of the author. The model under consideration indeed describes the free gas of massless particles in a one-dimensional environment. This investigation can have consequences in two fundamental respects. The first one concerns the applicability of the (block-)monotone statistics to concrete physical models, yet completely unknown. Since the formula for the degeneracy of the energy-levels of the one-particle Hamiltonian of a free particle is very involved, the second aspect might be related to the, highly nontrivial, investigation of the expected thermodynamics of the free gas of particles obeying the block-monotone statistics in arbitrary spatial dimensions. A final section contains a comparison between the various (block, strict, and weak) monotone schemes with the Boltzmann statistics, which describes the gas of classical particles. It is seen that the block-monotone statistics, which takes into account the degeneracy of the energy-levels, seems the unique one having realistic physical applications. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
17 pages, 4797 KiB  
Article
Unstable Points, Ergodicity and Born’s Rule in 2d Bohmian Systems
by Athanasios C. Tzemos and George Contopoulos
Entropy 2023, 25(7), 1089; https://doi.org/10.3390/e25071089 - 20 Jul 2023
Cited by 2 | Viewed by 764
Abstract
We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of [...] Read more.
We study the role of unstable points in the Bohmian flow of a 2d system composed of two non-interacting harmonic oscillators. In particular, we study the unstable points in the inertial frame of reference as well as in the frame of reference of the moving nodal points, in cases with 1, 2 and multiple nodal points. Then, we find the contributions of the ordered and chaotic trajectories in the Born distribution, and when the latter is accessible by an initial particle distribution which does not satisfy Born’s rule. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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12 pages, 251 KiB  
Article
Quantum Mechanical Approach to the Khintchine and Bochner Criteria for Characteristic Functions
by Leon Cohen
Entropy 2023, 25(7), 1042; https://doi.org/10.3390/e25071042 - 11 Jul 2023
Viewed by 577
Abstract
While it is generally accepted that quantum mechanics is a probability theory, its methods differ radically from standard probability theory. We use the methods of quantum mechanics to understand some fundamental aspects of standard probability theory. We show that wave functions and operators [...] Read more.
While it is generally accepted that quantum mechanics is a probability theory, its methods differ radically from standard probability theory. We use the methods of quantum mechanics to understand some fundamental aspects of standard probability theory. We show that wave functions and operators do appear in standard probability theory. We do so by generalizing the Khintchine and Bochner criteria for a complex function to be a characteristic function. We show that quantum mechanics clarifies these criteria and suggests generalizations of them. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
23 pages, 2881 KiB  
Article
Differential Shannon Entropies Characterizing Electron–Nuclear Dynamics and Correlation: Momentum-Space Versus Coordinate-Space Wave Packet Motion
by Peter Schürger and Volker Engel
Entropy 2023, 25(7), 970; https://doi.org/10.3390/e25070970 - 23 Jun 2023
Cited by 1 | Viewed by 1062
Abstract
We calculate differential Shannon entropies derived from time-dependent coordinate-space and momentum-space probability densities. This is performed for a prototype system of a coupled electron–nuclear motion. Two situations are considered, where one is a Born–Oppenheimer adiabatic dynamics, and the other is a diabatic motion [...] Read more.
We calculate differential Shannon entropies derived from time-dependent coordinate-space and momentum-space probability densities. This is performed for a prototype system of a coupled electron–nuclear motion. Two situations are considered, where one is a Born–Oppenheimer adiabatic dynamics, and the other is a diabatic motion involving strong non-adiabatic transitions. The information about coordinate- and momentum-space dynamics derived from the total and single-particle entropies is discussed and interpreted with the help of analytical models. From the entropies, we derive mutual information, which is a measure for the electron–nuclear correlation. In the adiabatic case, it is found that such correlations are manifested differently in coordinate- and momentum space. For the diabatic dynamics, we show that it is possible to decompose the entropies into state-specific contributions. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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21 pages, 453 KiB  
Article
Winning a CHSH Game without Entangled Particles in a Finite Number of Biased Rounds: How Much Luck Is Needed?
by Christoph Gallus, Pawel Blasiak and Emmanuel M. Pothos
Entropy 2023, 25(5), 824; https://doi.org/10.3390/e25050824 - 21 May 2023
Cited by 1 | Viewed by 1401
Abstract
Quantum games, such as the CHSH game, are used to illustrate the puzzle and power of entanglement. These games are played over many rounds and in each round, the participants, Alice and Bob, each receive a question bit to which they each have [...] Read more.
Quantum games, such as the CHSH game, are used to illustrate the puzzle and power of entanglement. These games are played over many rounds and in each round, the participants, Alice and Bob, each receive a question bit to which they each have to give an answer bit, without being able to communicate during the game. When all possible classical answering strategies are analyzed, it is found that Alice and Bob cannot win more than 75% of the rounds. A higher percentage of wins arguably requires an exploitable bias in the random generation of the question bits or access to “non-local“ resources, such as entangled pairs of particles. However, in an actual game, the number of rounds has to be finite and question regimes may come up with unequal likelihood, so there is always a possibility that Alice and Bob win by pure luck. This statistical possibility has to be transparently analyzed for practical applications such as the detection of eavesdropping in quantum communication. Similarly, when Bell tests are used in macroscopic situations to investigate the connection strength between system components and the validity of proposed causal models, the available data are limited and the possible combinations of question bits (measurement settings) may not be controlled to occur with equal likelihood. In the present work, we give a fully self-contained proof for a bound on the probability to win a CHSH game by pure luck without making the usual assumption of only small biases in the random number generators. We also show bounds for the case of unequal probabilities based on results from McDiarmid and Combes and numerically illustrate certain exploitable biases. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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17 pages, 319 KiB  
Article
Dynamics of System States in the Probability Representation of Quantum Mechanics
by Vladimir N. Chernega and Olga V. Man’ko
Entropy 2023, 25(5), 785; https://doi.org/10.3390/e25050785 - 11 May 2023
Cited by 2 | Viewed by 1139
Abstract
A short description of the notion of states of quantum systems in terms of conventional probability distribution function is presented. The notion and the structure of entangled probability distributions are clarified. The evolution of even and odd Schrödinger cat states of the inverted [...] Read more.
A short description of the notion of states of quantum systems in terms of conventional probability distribution function is presented. The notion and the structure of entangled probability distributions are clarified. The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator. Evolution equations describing the time dependence of probability distributions identified with quantum system states are discussed. The connection with the Schrödinger equation and the von Neumann equation is clarified. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
20 pages, 923 KiB  
Article
Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis
by Bao Gia Bach, Akash Kundu, Tamal Acharya and Aritra Sarkar
Entropy 2023, 25(5), 763; https://doi.org/10.3390/e25050763 - 07 May 2023
Viewed by 2204
Abstract
This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of computation is defined. Classical and [...] Read more.
This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of computation is defined. Classical and quantum gate sets are compared to select some characteristic sets. The reachability and expressibility in a space-time-bounded setting for these gate sets are enumerated and visualized. These results are studied in terms of computational resources, universality, and quantum behavior. The article suggests how applications like geometric quantum machine learning, novel quantum algorithm synthesis, and quantum artificial general intelligence can benefit by studying circuit probabilities. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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37 pages, 2262 KiB  
Article
Non-Local Parallel Processing and Database Settlement Using Multiple Teleportation Followed by Grover Post-Selection
by Francisco Delgado and Carlos Cardoso-Isidoro
Entropy 2023, 25(2), 376; https://doi.org/10.3390/e25020376 - 18 Feb 2023
Cited by 1 | Viewed by 1288
Abstract
Quantum information applications emerged decades ago, initially introducing a parallel development that mimicked the approach and development of classical computer science. However, in the current decade, novel computer-science concepts were rapidly extended to the fields of quantum processing, computation, and communication. Thus, areas [...] Read more.
Quantum information applications emerged decades ago, initially introducing a parallel development that mimicked the approach and development of classical computer science. However, in the current decade, novel computer-science concepts were rapidly extended to the fields of quantum processing, computation, and communication. Thus, areas such as artificial intelligence, machine learning, and neural networks have their quantum versions; furthermore, the quantum brain properties of learning, analyzing, and gaining knowledge are discussed. Quantum properties of matter conglomerates have been superficially explored in such terrain; however, the settlement of organized quantum systems able to perform processing can open a new pathway in the aforementioned domains. In fact, quantum processing involves certain requisites as the settlement of copies of input information to perform differentiated processing developed far away or in situ to diversify the information stored there. Both tasks at the end provide a database of outcomes with which to perform either information matching or final global processing with at least a subset of those outcomes. When the number of processing operations and input information copies is large, parallel processing (a natural feature in quantum computation due to the superposition) becomes the most convenient approach to accelerate the database settlement of outcomes, thus affording a time advantage. In the current study, we explored certain quantum features to realize a speed-up model for the entire task of processing based on a common information input to be processed, diversified, and finally summarized to gain knowledge, either in pattern matching or global information availability. By using superposition and non-local properties, the most valuable features of quantum systems, we realized parallel local processing to set a large database of outcomes and subsequently used post-selection to perform an ending global processing or a matching of information incoming from outside. We finally analyzed the details of the entire procedure, including its affordability and performance. The quantum circuit implementation, along with tentative applications, were also discussed. Such a model could be operated between large processing technological systems using communication procedures and also on a moderately controlled quantum matter conglomerate. Certain interesting technical aspects involving the non-local control of processing via entanglement were also analyzed in detail as an associated but notable premise. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
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