Quantum Nonlocality Edited by Lev Vaidman Printed Edition of the Special Issue Published in Entropy www.mdpi.com/journal/entropy Quantum Nonlocality Quantum Nonlocality Special Issue Editor Lev Vaidman MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editor Lev Vaidman Tel Aviv University Israel 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) from 2018 to 2019 (available at: https://www.mdpi.com/journal/entropy/special issues/Quantum Nonlocality) 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 978-3-03897-948-7 (Pbk) ISBN 978-3-03897-949-4 (PDF) c 2019 by the authors. 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Contents About the Special Issue Editor ...................................... vii Lev Vaidman Quantum Nonlocality Reprinted from: Entropy 2019, 21, 447, doi:10.3390/e21050447 ..................... 1 Gilles Brassard and Paul Raymond-Robichaud Parallel Lives: A Local-Realistic Interpretation of “Nonlocal” Boxes Reprinted from: Entropy 2019, 21, 87, doi:10.3390/e21010087 ..................... 6 Daniel Rohrlich and Guy Hetzroni GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality Reprinted from: Entropy 2018, 20, 478, doi:10.3390/e20060478 ..................... 19 Allen Parks and Scott Spence Capacity and Entropy of a Retro-Causal Channel Observed in a Twin Mach-Zehnder Interferometer During Measurements of Pre- and Post-Selected Quantum Systems Reprinted from: Entropy 2018, 20, 411, doi:10.3390/e20060411 ..................... 27 Kishor Bharti, Maharshi Ray and Leong Chuan Kwek Non-Classical Correlations in n-Cycle Setting Reprinted from: Entropy 2019, 21, 134, doi:10.3390/e21020134 ..................... 34 Avishy Carmi and Eliahu Cohen On the Significance of the Quantum Mechanical Covariance Matrix Reprinted from: Entropy 2018, 20, 500, doi:10.3390/e20070500 ..................... 52 Ana C. S. Costa, Roope Uola and Otfried Guhne ¨ Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems Reprinted from: Entropy 2018, 2, 763, doi:10.3390/e20100763 ..................... 61 Yi-Zheng Zhen, Xin-Yu Xu, Li Li, Nai-Le Liu, Kai Chen The Einstein–Podolsky–Rosen Steering and Its Certification Reprinted from: Entropy 2019, 21, 422, doi:10.3390/e21040422 ..................... 88 Alberto Montina and Stefan Wolf Discrimination of Non-Local Correlations Reprinted from: Entropy 2019, 21, 104, doi:10.3390/e21020104 .....................110 Yeong-Cherng Liang and Yanbao Zhang Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing Reprinted from: Entropy 2019, 21, 185, doi:10.3390/e21020185 .....................132 Sergey A. Podoshvedov Efficient Quantum Teleportation of Unknown Qubit Based on DV-CV Interaction Mechanism Reprinted from: Entropy 2019, 21, 150, doi:10.3390/e21020150 .....................148 Emmanuel Zambrini Cruzeiro and Nicolas Gisin Bell Inequalities with One Bit of Communication Reprinted from: Entropy 2019, 21, 171, doi:10.3390/e21020171 .....................168 v G. S. Paraoanu Non-Local Parity Measurements and the Quantum Pigeonhole Effect Reprinted from: Entropy 2018, 20, 606, doi:10.3390/e20080606 .....................180 Alma Elena Piceno Mart´ınez, Ernesto Ben´ıtez Rodr´ıguez, Julio Abraham Mendoza Fierro, Marcela Maribel M´endez Otero and Luis Manuel Ar´evalo Aguilar Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment Reprinted from: Entropy 2018, 20, 299, doi:10.3390/e20040299 .....................186 Johann Summhammer, Georg Sulyok and Gustav Bernroider Quantum Dynamics and Non-Local Effects Behind Ion Transition States during Permeation in Membrane Channel Proteins Reprinted from: Entropy 2018, 20, 558, doi:10.3390/e20080558 .....................198 Rita Claudia Iotti and Fausto Rossi Microscopic Theory of Energy Dissipation and Decoherence in Solid-State Quantum Devices: Need for Nonlocal Scattering Models Reprinted from: Entropy 2018, 20, 726, doi:10.3390/e20100726 .....................211 vi About the Special Issue Editor Lev Vaidman was born in Leningrad and studied physics in Israel. He received his Ph.D. from Tel Aviv University under the guidance of Yakir Aharonov, with whom he continues to collaborate until today. After three years at University of South Carolina, he returned to Tel Aviv, where he became head of a quantum research group. His research is centered upon the foundations of quantum mechanics and quantum information. Vaidman is a theoretical physicist, and many of his proposals have been implemented in laboratories around the world, though he himself only became recently involved in the experimental realizations of his ideas. Vaidman is mainly known for introducing teleportation of continuous variables, cryptography with orthogonal states, novel types of quantum measurement (nonlocal, weak, protective, interaction-free), and introducing numerous quantum paradoxes. His analyses of quantum mechanical interpretations are centered in the development of the many-worlds interpretation, for which he is apparently the strongest proponent. vii entropy Editorial Quantum Nonlocality Lev Vaidman Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel; [email protected]; Tel.: +972-545908806 Received: 23 April 2019; Accepted: 24 April 2019; Published: 29 April 2019 Keywords: nonlocality; entanglement; quantum The role of physics is to explain observed phenomena. Explanation in physics began as a causal chain of local actions. The first nonlocal action was Newton’s law of gravity, but Newton himself considered the nonlocal action to be something completely absurd which could not be true—and indeed, gravity today is explained through local action of the gravitational field. It is the quantum theory which made physicists believe that there was nonlocality in Nature. It also led to the acceptance of randomness in Nature, the existence of which is considered as another weakness of science today. In fact, I hope that it is possible to remove randomness and nonlocality from our description of Nature [1]. Accepting the existence of parallel worlds [2] eliminates randomness and avoids action at a distance, but it still does not remove nonlocality. This special issue of Entropy is an attempt to more deeply understand the nonlocality of the quantum theory. I am interested to explore the chances of removing nonlocality from the quantum theory, and such an attempt is the most desirable contribution to this special issue; however, other works presented here which characterize the quantum nonlocality and investigate the role of nonlocality as an explanation of observed phenomena also shed light on this question. It is important to understand what the meaning of nonlocality is in quantum theory. Quantum theory does not have the strongest and simplest concept of nonlocality, which is the possibility of making an instantaneous observable local change at a distance. However, all single-world interpretations do have actions at a distance. The quantum nonlocality also has an operational meaning for us, local observers, who can live only in a single world. Given entangled particles placed at a distance, a measurement on one of the particles instantaneously changes the quantum state of the other, from a density matrix to a pure state. It is only in the framework of the many-worlds interpretation, considering all worlds together, where the measurement causes no change in the remote particle, and it remains to be described by a density matrix. Another apparent nonlocality aspect is the existence of global topological features, such as the Aharonov-Bohm effect [3]. I believe I succeeded in removing this kind of nonlocality from quantum mechanics [4], but the issue is still controversial [5–8]. Unfortunately, no contributions clarifying this problem appear in this issue. It is of interest to analyze nonlocal properties of composite quantum systems, the properties of systems in separate locations [9]. These properties are nonlocal by definition, and the nonlocality of their description does not necessarily tell us that the Nature is nonlocal. It is not surprising that nonlocal properties obey nonlocal dynamical equations. Although unrelated to the question of nonlocality in Nature, it is a useful tool for quantum information which, due to quantum technology revolution, becomes not just the future, but the present of practical applications. See the discussion of this aspect of quantum nonlolcality in this issue and note the recent first experimental realization of measurements of nonlocal variables [10]. For the problem of nonlocality of Nature, the important question is: which of the nonlocal features of composite systems cannot be specified by local measurements of its parts? More precisely, this is the question of nonlocality of a single world, would it