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Entropy in Foundations of Quantum Physics
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Entropy in Foundations of Quantum Physics

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

Deadline for manuscript submissions: closed (31 May 2019) | Viewed by 51830

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Marcin Pawłowski

E-Mail Website
Guest Editor
Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
Interests: foundations of physics; cryptography; nonlocality; quantum information

Special Issue Information

Dear Colleagues,

Recently, the interest in foundational research in physics has been rekindled, mostly due to the advances of quantum information. Not only does it provide versatile tools, but also ways to link this field with practical applications. Probably, the best example of such a connection is Ekert’s cryptographic protocol from 1991.

Since entropy can be used, among other things, to measure uncertainty and information capacity, it has been widely used in that field. Some of its applications include Bell inequalities, nonlocality, causal structures, system complexity and uncertainty relations. Moreover, presence of entropy in other areas of research allows it to become a bridge between foundations and these fields.

Current trends seem to indicate that the role of entropy in the studies of the foundations of quantum physics will only increase and lead to many new exciting discoveries. I, therefore, encourage you to submit your work to this Special Issue.

Dr. Marcin Pawłowski
Guest Editor

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

  • Entropy
  • Uncertainty relations
  • Information causality
  • Bell inequalities
  • Causal structures
  • Axioms of quantum mechanics
  • Nonlocality
  • Contextuality

Published Papers (16 papers)

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Editorial

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4 pages, 175 KiB  
Editorial
Entropy in Foundations of Quantum Physics
by Marcin Pawłowski
Entropy 2020, 22(3), 371; https://doi.org/10.3390/e22030371 - 24 Mar 2020
Viewed by 2836
Abstract
Entropy can be used in studies on foundations of quantum physics in many different ways, each of them using different properties of this mathematical object [...] Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

Research

Jump to: Editorial

20 pages, 410 KiB  
Article
Hypergraph Contextuality
by Mladen Pavičić
Entropy 2019, 21(11), 1107; https://doi.org/10.3390/e21111107 - 12 Nov 2019
Cited by 8 | Viewed by 2579
Abstract
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum [...] Read more.
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum contextuality for any quantum state of a given dimension. There are two major classes of state-independent contextual sets—the Kochen-Specker ones and the operator-based ones. In this paper, we present a third, hypergraph-based class of contextual sets. Hypergraph inequalities serve as a measure of contextuality. We limit ourselves to qutrits and obtain thousands of 3-dim contextual sets. The simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation. They also enable establishing new entropic contextualities. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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37 pages, 397 KiB  
Article
The Entropic Dynamics Approach to Quantum Mechanics
by Ariel Caticha
Entropy 2019, 21(10), 943; https://doi.org/10.3390/e21100943 - 26 Sep 2019
Cited by 18 | Viewed by 2865
Abstract
Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified [...] Read more.
Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures—which is a Hamilton-Killing flow in phase space—is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
12 pages, 317 KiB  
Article
A New Mechanism of Open System Evolution and Its Entropy Using Unitary Transformations in Noncomposite Qudit Systems
by Julio A. López-Saldívar, Octavio Castaños, Margarita A. Man’ko and Vladimir I. Man’ko
Entropy 2019, 21(8), 736; https://doi.org/10.3390/e21080736 - 27 Jul 2019
Cited by 9 | Viewed by 2376
Abstract
The evolution of an open system is usually associated with the interaction of the system with an environment. A new method to study the open-type system evolution of a qubit (two-level atom) state is established. This evolution is determined by a unitary transformation [...] Read more.
The evolution of an open system is usually associated with the interaction of the system with an environment. A new method to study the open-type system evolution of a qubit (two-level atom) state is established. This evolution is determined by a unitary transformation applied to the qutrit (three-level atom) state, which defines the qubit subsystems. This procedure can be used to obtain different qubit quantum channels employing unitary transformations into the qutrit system. In particular, we study the phase damping and spontaneous-emission quantum channels. In addition, we mention a proposal for quasiunitary transforms of qubits, in view of the unitary transform of the total qutrit system. The experimental realization is also addressed. The probability representation of the evolution and its information-entropic characteristics are considered. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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15 pages, 364 KiB  
Article
Uniqueness of Minimax Strategy in View of Minimum Error Discrimination of Two Quantum States
by Jihwan Kim, Donghoon Ha and Younghun Kwon
Entropy 2019, 21(7), 671; https://doi.org/10.3390/e21070671 - 09 Jul 2019
Cited by 4 | Viewed by 2988
Abstract
This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the [...] Read more.
This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the receiver may obtain the minimum information about quantum states, but the receiver performs an optimal measurement to obtain guessing probability for the quantum ensemble prepared by the sender. Therefore, knowing whether the optimal strategy of the game is unique is essential. This is because there is no alternative if the optimal strategy is unique. This paper proposes the necessary and sufficient condition for an optimal strategy of the sender to be unique. Also, we investigate the quantum states that exhibit the minimum guessing probability when a sender’s minimax strategy is unique. Furthermore, we show that a sender’s minimax strategy and a receiver’s minimum error strategy cannot be unique if one can simultaneously diagonalize two quantum states, with the optimal measurement of the minimax strategy. This implies that a sender can confirm that the optimal strategy of only a single side (a sender or a receiver but not both of them) is unique by preparing specific quantum states. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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15 pages, 1061 KiB  
Article
Improving Parameter Estimation of Entropic Uncertainty Relation in Continuous-Variable Quantum Key Distribution
by Ziyang Chen, Yichen Zhang, Xiangyu Wang, Song Yu and Hong Guo
Entropy 2019, 21(7), 652; https://doi.org/10.3390/e21070652 - 02 Jul 2019
Cited by 21 | Viewed by 2894
Abstract
The entropic uncertainty relation (EUR) is of significant importance in the security proof of continuous-variable quantum key distribution under coherent attacks. The parameter estimation in the EUR method contains the estimation of the covariance matrix (CM), as well as the max-entropy. The discussions [...] Read more.
The entropic uncertainty relation (EUR) is of significant importance in the security proof of continuous-variable quantum key distribution under coherent attacks. The parameter estimation in the EUR method contains the estimation of the covariance matrix (CM), as well as the max-entropy. The discussions in previous works have not involved the effect of finite-size on estimating the CM, which will further affect the estimation of leakage information. In this work, we address this issue by adapting the parameter estimation technique to the EUR analysis method under composable security frameworks. We also use the double-data modulation method to improve the parameter estimation step, where all the states can be exploited for both parameter estimation and key generation; thus, the statistical fluctuation of estimating the max-entropy disappears. The result shows that the adapted method can effectively estimate parameters in EUR analysis. Moreover, the double-data modulation method can, to a large extent, save the key consumption, which further improves the performance in practical implementations of the EUR. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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13 pages, 305 KiB  
Article
On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State
by Lu Wei
Entropy 2019, 21(5), 539; https://doi.org/10.3390/e21050539 - 27 May 2019
Cited by 16 | Viewed by 3000
Abstract
The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an [...] Read more.
The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
11 pages, 1030 KiB  
Article
Probabilistic Resumable Quantum Teleportation of a Two-Qubit Entangled State
by Zhan-Yun Wang, Yi-Tao Gou, Jin-Xing Hou, Li-Ke Cao and Xiao-Hui Wang
Entropy 2019, 21(4), 352; https://doi.org/10.3390/e21040352 - 01 Apr 2019
Cited by 7 | Viewed by 3283
Abstract
We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially [...] Read more.
We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially entangled particles. However, the two-qubit entangled state to be teleported will be destroyed if teleportation fails. To solve this problem, we show a more sophisticated probabilistic resumable quantum teleportation scheme of a two-qubit entangled state, where the state to be teleported can be recovered by the sender when teleportation fails. Thus the information of the unknown state is retained during the process. Accordingly, we can repeat the teleportion process as many times as one has available quantum channels. Therefore, the quantum channels with weak entanglement can also be used to teleport unknown two-qubit entangled states successfully with a high number of repetitions, and for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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12 pages, 1274 KiB  
Article
Quantum Discord, Thermal Discord, and Entropy Generation in the Minimum Error Discrimination Strategy
by Omar Jiménez, Miguel Angel Solís-Prosser, Leonardo Neves and Aldo Delgado
Entropy 2019, 21(3), 263; https://doi.org/10.3390/e21030263 - 08 Mar 2019
Cited by 6 | Viewed by 4542
Abstract
We study the classical and quantum correlations in the minimum error discrimination (ME) of two non-orthogonal pure quantum states. In particular, we consider quantum discord, thermal discord and entropy generation. We show that ME allows one to reach the accessible information between the [...] Read more.
We study the classical and quantum correlations in the minimum error discrimination (ME) of two non-orthogonal pure quantum states. In particular, we consider quantum discord, thermal discord and entropy generation. We show that ME allows one to reach the accessible information between the two involved parties, Alice and Bob, in the discrimination process. We determine the amount of quantum discord that is consumed in the ME and show that the entropy generation is, in general, higher than the thermal discord. However, in certain cases the entropy generation is very close to thermal discord, which indicates that, in these cases, the process generates the least possible entropy. Moreover, we also study the ME process as a thermodynamic cycle and we show that it is in agreement with the second law of thermodynamics. Finally, we study the relation between the accessible information and the optimum success probability in ME. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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28 pages, 867 KiB  
Article
Representation Lost: The Case for a Relational Interpretation of Quantum Mechanics
by Raffael Krismer
Entropy 2018, 20(12), 975; https://doi.org/10.3390/e20120975 - 15 Dec 2018
Cited by 7 | Viewed by 3468
Abstract
Contemporary non-representationalist interpretations of the quantum state (especially QBism, neo-Copenhagen views, and the relational interpretation) maintain that quantum states codify observer-relative information. This paper provides an extensive defense of such views, while emphasizing the advantages of, specifically, the relational interpretation. [...] Read more.
Contemporary non-representationalist interpretations of the quantum state (especially QBism, neo-Copenhagen views, and the relational interpretation) maintain that quantum states codify observer-relative information. This paper provides an extensive defense of such views, while emphasizing the advantages of, specifically, the relational interpretation. The argument proceeds in three steps: (1) I present a classical example (which exemplifies the spirit of the relational interpretation) to illustrate why some of the most persistent charges against non-representationalism have been misguided. (2) The special focus is placed on dynamical evolution. Non-representationalists often motivate their views by interpreting the collapse postulate as the quantum mechanical analogue of Bayesian probability updating. However, it is not clear whether one can also interpret the Schrödinger equation as a form of rational opinion updating. Using results due to Hughes & van Fraassen as well as Lisi, I argue that unitary evolution has a counterpart in classical probability theory: in both cases (quantum and classical) probabilities relative to a non-participating observer evolve according to an entropy maximizing principle (and can be interpreted as rational opinion updating). (3) Relying on a thought-experiment by Frauchiger and Renner, I discuss the differences between quantum and classical probability models. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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15 pages, 952 KiB  
Article
Some Consequences of the Thermodynamic Cost of System Identification
by Chris Fields
Entropy 2018, 20(10), 797; https://doi.org/10.3390/e20100797 - 17 Oct 2018
Cited by 15 | Viewed by 3375
Abstract
The concept of a “system” is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which “pointer state” measurements are to be made. [...] Read more.
The concept of a “system” is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which “pointer state” measurements are to be made. It is shown that system identification is at best approximate, even in a finite world, and that violations of the Leggett–Garg and Bell/CHSH (Clauser-Horne-Shimony-Holt) inequalities emerge naturally as requirements for successful system identification. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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15 pages, 2738 KiB  
Article
Image Thresholding Segmentation on Quantum State Space
by Xiangluo Wang, Chunlei Yang, Guo-Sen Xie and Zhonghua Liu
Entropy 2018, 20(10), 728; https://doi.org/10.3390/e20100728 - 23 Sep 2018
Cited by 10 | Viewed by 4148
Abstract
Aiming to implement image segmentation precisely and efficiently, we exploit new ways to encode images and achieve the optimal thresholding on quantum state space. Firstly, the state vector and density matrix are adopted for the representation of pixel intensities and their probability distribution, [...] Read more.
Aiming to implement image segmentation precisely and efficiently, we exploit new ways to encode images and achieve the optimal thresholding on quantum state space. Firstly, the state vector and density matrix are adopted for the representation of pixel intensities and their probability distribution, respectively. Then, the method based on global quantum entropy maximization (GQEM) is proposed, which has an equivalent object function to Otsu’s, but gives a more explicit physical interpretation of image thresholding in the language of quantum mechanics. To reduce the time consumption for searching for optimal thresholds, the method of quantum lossy-encoding-based entropy maximization (QLEEM) is presented, in which the eigenvalues of density matrices can give direct clues for thresholding, and then, the process of optimal searching can be avoided. Meanwhile, the QLEEM algorithm achieves two additional effects: (1) the upper bound of the thresholding level can be implicitly determined according to the eigenvalues; and (2) the proposed approaches ensure that the local information in images is retained as much as possible, and simultaneously, the inter-class separability is maximized in the segmented images. Both of them contribute to the structural characteristics of images, which the human visual system is highly adapted to extract. Experimental results show that the proposed methods are able to achieve a competitive quality of thresholding and the fastest computation speed compared with the state-of-the-art methods. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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14 pages, 523 KiB  
Article
Quantum Quantifiers for an Atom System Interacting with a Quantum Field Based on Pseudoharmonic Oscillator States
by Bahaaudin Mohammadnoor Raffah and Kamal Berrada
Entropy 2018, 20(8), 607; https://doi.org/10.3390/e20080607 - 16 Aug 2018
Cited by 4 | Viewed by 3050
Abstract
We develop a useful model considering an atom-field system interaction in the framework of pseudoharmonic oscillators. We examine qualitatively the different physical quantities for a two-level atom (TLA) system interacting with a quantized coherent field in the context of photon-added coherent states of [...] Read more.
We develop a useful model considering an atom-field system interaction in the framework of pseudoharmonic oscillators. We examine qualitatively the different physical quantities for a two-level atom (TLA) system interacting with a quantized coherent field in the context of photon-added coherent states of pseudoharmonic oscillators. Using these coherent states, we solve the model that exhibits the interaction between the TLA and field associated with these kinds of potentials. We analyze the temporal evolution of the entanglement, statistical properties, geometric phase and squeezing entropies. Finally, we show the relationship between the physical quantities and their dynamics in terms of the physical parameters. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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12 pages, 1194 KiB  
Article
Enhancing of Self-Referenced Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction
by Hai Zhong, Yijun Wang, Xudong Wang, Qin Liao, Xiaodong Wu and Ying Guo
Entropy 2018, 20(8), 578; https://doi.org/10.3390/e20080578 - 06 Aug 2018
Cited by 10 | Viewed by 2925
Abstract
The scheme of the self-referenced continuous-variable quantum key distribution (SR CV-QKD) has been experimentally demonstrated. However, because of the finite dynamics of Alice’s amplitude modulator, there will be an extra excess noise that is proportional to the amplitude of the reference pulse, while [...] Read more.
The scheme of the self-referenced continuous-variable quantum key distribution (SR CV-QKD) has been experimentally demonstrated. However, because of the finite dynamics of Alice’s amplitude modulator, there will be an extra excess noise that is proportional to the amplitude of the reference pulse, while the maximal transmission distance of this scheme is positively correlated with the amplitude of the reference pulse. Therefore, there is a trade-off between the maximal transmission distance and the amplitude of the reference pulse. In this paper, we propose the scheme of SR CV-QKD with virtual photon subtraction, which not only has no need for the use of a high intensity reference pulse to improve the maximal transmission distance, but also has no demand of adding complex physical operations to the original self-referenced scheme. Compared to the original scheme, our simulation results show that a considerable extension of the maximal transmission distance can be obtained when using a weak reference pulse, especially for one-photon subtraction. We also find that our scheme is sensible with the detector’s electronic noise at reception. A longer maximal transmission distance can be achieved for lower electronic noise. Moreover, our scheme has a better toleration of excess noise compared to the original self-referenced scheme, which implies the advantage of using virtual photon subtraction to increase the maximal tolerable excess noise for distant users. These results suggest that our scheme can make the SR CV-QKD from the laboratory possible for practical metropolitan area application. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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13 pages, 6268 KiB  
Article
Security Analysis of Unidimensional Continuous-Variable Quantum Key Distribution Using Uncertainty Relations
by Pu Wang, Xuyang Wang and Yongmin Li
Entropy 2018, 20(3), 157; https://doi.org/10.3390/e20030157 - 01 Mar 2018
Cited by 9 | Viewed by 3436
Abstract
We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using [...] Read more.
We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using the Heisenberg uncertainty relation, respectively. We also present a method to increase both the secret key rates and maximal transmission distances of the UD coherent-state protocol by adding an optimal noise to the reconciliation side. It is expected that our analysis will aid in the practical applications of the UD protocol. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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12 pages, 389 KiB  
Article
Tsirelson’s Bound Prohibits Communication through a Disconnected Channel
by Avishy Carmi and Daniel Moskovich
Entropy 2018, 20(3), 151; https://doi.org/10.3390/e20030151 - 27 Feb 2018
Cited by 5 | Viewed by 3295
Abstract
Why does nature only allow nonlocal correlations up to Tsirelson’s bound and not beyond? We construct a channel whose input is statistically independent of its output, but through which communication is nevertheless possible if and only if Tsirelson’s bound is violated. This provides [...] Read more.
Why does nature only allow nonlocal correlations up to Tsirelson’s bound and not beyond? We construct a channel whose input is statistically independent of its output, but through which communication is nevertheless possible if and only if Tsirelson’s bound is violated. This provides a statistical justification for Tsirelson’s bound on nonlocal correlations in a bipartite setting. Full article
(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)
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