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Special Issue "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: 31 May 2019

Special Issue Editor

Guest Editor
Dr. Marcin Pawłowski

Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
Website | E-Mail
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 papers will be 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 1600 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 (9 papers)

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Research

Open AccessArticle Probabilistic Resumable Quantum Teleportation of a Two-Qubit Entangled State
Entropy 2019, 21(4), 352; https://doi.org/10.3390/e21040352
Received: 7 February 2019 / Revised: 23 March 2019 / Accepted: 25 March 2019 / Published: 1 April 2019
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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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Open AccessArticle Quantum Discord, Thermal Discord, and Entropy Generation in the Minimum Error Discrimination Strategy
Entropy 2019, 21(3), 263; https://doi.org/10.3390/e21030263
Received: 25 January 2019 / Revised: 22 February 2019 / Accepted: 1 March 2019 / Published: 8 March 2019
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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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Open AccessArticle Representation Lost: The Case for a Relational Interpretation of Quantum Mechanics
Entropy 2018, 20(12), 975; https://doi.org/10.3390/e20120975
Received: 26 October 2018 / Revised: 2 December 2018 / Accepted: 11 December 2018 / Published: 15 December 2018
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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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Open AccessArticle Some Consequences of the Thermodynamic Cost of System Identification
Entropy 2018, 20(10), 797; https://doi.org/10.3390/e20100797
Received: 17 August 2018 / Revised: 23 September 2018 / Accepted: 15 October 2018 / Published: 17 October 2018
Cited by 1 | PDF Full-text (952 KB) | HTML Full-text | XML Full-text
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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Open AccessArticle Image Thresholding Segmentation on Quantum State Space
Entropy 2018, 20(10), 728; https://doi.org/10.3390/e20100728
Received: 5 August 2018 / Revised: 11 September 2018 / Accepted: 20 September 2018 / Published: 23 September 2018
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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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Open AccessArticle Quantum Quantifiers for an Atom System Interacting with a Quantum Field Based on Pseudoharmonic Oscillator States
Entropy 2018, 20(8), 607; https://doi.org/10.3390/e20080607
Received: 9 June 2018 / Revised: 17 July 2018 / Accepted: 2 August 2018 / Published: 16 August 2018
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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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Open AccessArticle Enhancing of Self-Referenced Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction
Entropy 2018, 20(8), 578; https://doi.org/10.3390/e20080578
Received: 28 June 2018 / Revised: 26 July 2018 / Accepted: 2 August 2018 / Published: 6 August 2018
Cited by 1 | PDF Full-text (1194 KB) | HTML Full-text | XML Full-text
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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Open AccessArticle Security Analysis of Unidimensional Continuous-Variable Quantum Key Distribution Using Uncertainty Relations
Entropy 2018, 20(3), 157; https://doi.org/10.3390/e20030157
Received: 30 January 2018 / Revised: 22 February 2018 / Accepted: 27 February 2018 / Published: 1 March 2018
Cited by 2 | PDF Full-text (6268 KB) | HTML Full-text | XML Full-text
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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Open AccessArticle Tsirelson’s Bound Prohibits Communication through a Disconnected Channel
Entropy 2018, 20(3), 151; https://doi.org/10.3390/e20030151
Received: 4 December 2017 / Revised: 18 February 2018 / Accepted: 24 February 2018 / Published: 27 February 2018
Cited by 1 | PDF Full-text (389 KB) | HTML Full-text | XML Full-text
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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