Entropy in Foundations of Quantum Physics • Marcin Pawłowski Entropy in Foundations of Quantum Physics Edited by Marcin Pawłowski Printed Edition of the Special Issue Published in Entropy www.mdpi.com/journal/entropy Entropy in Foundations of Quantum Physics Entropy in Foundations of Quantum Physics Special Issue Editor Marcin Pawłowski MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Special Issue Editor Marcin Pawłowski University of Gdansk´ Poland Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Entropy (ISSN 1099-4300) (available at: https://www.mdpi.com/journal/entropy/special issues/ Foundations Quantum Physics). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03928-951-6 (Pbk) ISBN 978-3-03928-952-3 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii Marcin Pawłowski Entropy in Foundations of Quantum Physics Reprinted from: Entropy 2020, 22, 371, doi:10.3390/e22030371 ..................... 1 Mladen Paviˇci´c Hypergraph Contextuality Reprinted from: Entropy 2019, 21, 1107, doi:10.3390/e211111075 ................... 5 Ariel Caticha The Entropic Dynamics Approach to Quantum Mechanics Reprinted from: Entropy 2019, 21, 943, doi:10.3390/e21100943 .................... 25 Julio A. L´opez-Sald´ıvar, Octavio Casta ˜nos,Margarita A. Man’ko and Vladimir I. Man’ko A New Mechanism of Open System Evolution and Its Entropy Using Unitary Transformations in Noncomposite Qudit Systems Reprinted from: Entropy 2019, 21, 736, doi:10.3390/e21080736 ..................... 63 Jihwan Kim, Donghoon Ha and Younghun Kwon Uniqueness of Minimax Strategy in View of Minimum Error Discrimination of Two Quantum States Reprinted from: Entropy 2019, 21, 671, doi:10.3390/e21070671 .................... 75 Ziyang Chen, Yichen Zhang, Xiangyu Wang, Song Yu and Hong Guo Improving Parameter Estimation ofEntropic Uncertainty Relation in Continuous-Variable Quantum Key Distribution Reprinted from: Entropy 2019, 21, , doi:10.3390/e21070652 ....................... 91 Lu Wei On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State Reprinted from: Entropy 2019, 21, 539, doi:10.3390/e21050539 .....................107 Zhan-Yun Wang, Yi-Tao Gou, Jin-Xing Hou, Li-Ke Cao and Xiao-Hui Wang Probabilistic Resumable Quantum Teleportation of a Two-Qubit Entangled State Reprinted from: Entropy 2019, 21, 352, doi:10.3390/e21040352 .....................121 Omar Jim´enez,Miguel Angel Sol´ıs-Prosser, Leonardo Neves and Aldo Delgado Quantum Discord, Thermal Discord, and Entropy Generation in the Minimum Error Discrimination Strategy Reprinted from: Entropy 2019, 21, 263, doi:10.3390/e21030263 .....................133 Raffael Krismer Representation Lost: The Case for a Relational Interpretation of Quantum Mechanics Reprinted from: Entropy 2018, 20, 975, doi:10.3390/e20120975 ....................145 Chris Fields Some Consequences of the Thermodynamic Cost of System Identification Reprinted from: Entropy 2018, 20, 797, doi:10.3390/e201007975 ....................173 v Xiangluo Wang, Chunlei Yang, Guo-Sen Xie and Zhonghua Liu Image Thresholding Segmentation on Quantum State Space Reprinted from: Entropy 2018, 20, 728, doi:10.3390/e20100728 .....................189 Bahaaudin Mohammadnoor Raffah, Kamal Berrada Quantum Quantifiers for an Atom System Interacting with a Quantum FieldBased on Pseudoharmonic Oscillator States Reprinted from: Entropy 2018, 20, 607, doi:10.3390/e20080607 .....................205 Hai Zhong, Yijun Wang, Xudong Wang, Qin Liao, Xiaodong Wu and Ying Guo Enhancing of Self-Referenced Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction Reprinted from: Entropy 2018, 20, 578, doi:10.3390/e20080578 .....................219 Pu Wang, Xuyang Wang and Yongmin Li Security Analysis of Unidimensional Continuous-Variable Quantum Key Distribution Using Uncertainty Relations Reprinted from: Entropy 2018, 20, 157, doi:10.3390/e20030157 .....................231 Avishy Carmi and Daniel Moskovich Tsirelson’s Bound Prohibits Communication through a Disconnected Channel Reprinted from: Entropy 2018, 20, 151, doi:10.3390/e20030151 .....................245 vi About the Special Issue Editor Marcin Pawłowski, Ph.D., began his studies in economics in Gdansk,´ Poland. He later switched to physics and obtained his Ph.D. in 2010 followed by a Postdoctoral position at University of Bristol. He returned to the University of Gdansk´ in 2013 to start his own research group, which he has been running since. Right now, his Quantum Cybersecurity group is a part of International Centre for Theory of Quantum Technologies. Apart from problems in theoretical and applied quantum cryptography and communication, the group studies fundamental aspects of quantum physics which have a basis in all applications. vii entropy Editorial Entropy in Foundations of Quantum Physics Marcin Pawłowski International Centre for Theory of Quantum Technologies, University of Gda´nsk, 80-952 Gda´nsk, Poland; [email protected] Received: 18 March 2020; Accepted: 19 March 2020; Published: 24 March 2020 Keywords: foundations of quantum mechanics; quantum cryptography; entropy 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. First of all, entropy can be intuitively understood and we can exploit that fact by finding ways to derive predictions of quantum mechanics without employing the full mathematical apparatus of that theory. Instead, we can propose operational axioms which we can more easily understand and try to find the reasons why the universe behaves in the way that it does. The second reason for its usefulness stems simply from how convenient it is to use entropy in different aspects of information processing. It is therefore an indispensable tool for quantum information theory, which recently has been the field that led to the most breakthroughs in foundations of physics. Finally, sheer ubiquity of entropy in physics and other fields makes it a possible bridge between different areas, enabling us to carry insights from one to another. In this Special Issue, we find examples of papers which employ each of these approaches. In the paper “Hypergraph Contextuality” [1], the author introduces a new form of quantum contextuality. The two previously known forms were Kochen–Specker (KS) [2] and observable-based [3] contextualities. In paper [1], hypergraphs with 3-dim vectors are considered, in which some of those vectors that belong to only one triplet are dropped, as in the observable approach, and smaller hypergraphs are generated from them, such that one cannot assign definite binary values to them, as in the KS approach. This new approach is called hypergraph contextuality and allows us, among other things, to establish new entropic contextualities. In the paper “The Entropic Dynamics Approach to Quantum Mechanics” [4], the author develops his theory of Entropic Dynamics introduced in [5–7]. In this paper [4], A new version of Entropic Dynamics is introduced in which particles follow smooth differentiable Brownian trajectories in order 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. In the paper “A New Mechanism of Open System Evolution and Its Entropy Using Unitary Transformations in Noncomposite Qudit Systems” [8], the authors develop further their method introduced in [9], which models the dynamics of open system evolution of qubits by the unitary evolution of qutrits instead of by composite systems as it is usually done. In particular, they apply their methodology to study the behavior of phase damping and spontaneous emission channels and compute the evolution of the state’s entropy in these channels. In the paper “Uniqueness of Minimax Strategy in View of Minimum Error Discrimination of Two Quantum States” [10], the authors consider minimum error discrimination of two quantum sates as a game. This is not a new approach; however, in this paper [10], it is generalized to take into account different prior probabilities for the states, choosing which constitutes the sender’s strategy. They are able to obtain the necessary and sufficient condition for the uniqueness of it. They also provide a condition for when the sender’s minimax strategy and the receiver’s optimal minimum error strategy cannot both be unique. Entropy 2020, 22, 371; doi:10.3390/e220303711 www.mdpi.com/journal/entropy Entropy 2020, 22, 371 Paper [11] deals with the issue of parameter estimation in continuous variable QKD. This is very simple problem with a straightforward solution if we work in an asymptotic limit. This is, however, not very practical and