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Quantum Foundations 90 Years of Uncertainty Quantum Foundations 90 Years of Uncertainty Edited by Pedro W. Lamberti, Gustavo M. Bosyk, Sebastian Fortin and Federico Holik Printed Edition of the Special Issue Published in Entropy www.mdpi.com/journal/entropy Quantum Foundations Quantum Foundations 90 Years of Uncertainty Special Issue Editors Pedro W. Lamberti Gustavo M. Bosyk Sebastian Fortin Federico Holik MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editors Pedro W. Lamberti Gustavo M. Bosyk Universidad Nacional de Cordoba´ & CONICET Instituto de F´ısica La Plata Argentina Argentina Sebastian Fortin Universidad de Buenos Aires Argentina Federico Holik Instituto de F´ısica La Plata Argentina 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/90 Years Uncertainty) 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 978-3-03897-754-4 (Pbk) ISBN 978-3-03897-755-1 (PDF) c 2019 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 Editors ..................................... vii Gustavo M. Bosyk , Sebastian Fortin, Federico Holik and Pedro W. Lamberti Special Issue “Quantum Foundations: 90 Years of Uncertainty” Reprinted from: Entropy 2019, 21, 159, doi:10.3390/e21020159 ..................... 1 Andrei Y. Khrennikov and Elena R. Loubenets Evaluating the Maximal Violation of the Original Bell Inequality byTwo-Qudit States Exhibiting Perfect Correlations/Anticorrelations Reprinted from: Entropy 2018, 20, 829, doi:10.3390/e20110829 ..................... 4 Claudia Zander and Angel Ricardo Plastino Revisiting Entanglement within the Bohmian Approach to Quantum Mechanics Reprinted from: Entropy 2018, 20, 473, doi:10.3390/e20060473 ..................... 19 Karl Svozil New Forms of Quantum Value Indefiniteness Suggest That Incompatible Views on Contexts Are Epistemic Reprinted from: Entropy 2018, 20, 406, doi:10.3390/e20060406 ..................... 38 Jeremy Liu, Federico Spedalieri, Ke-Thia Yao, Thomas E. Potok, Catherine Schuman, Steven Young, Garrett S. Rose, and Gangotree Chamka Adiabatic Quantum Computation Applied to Deep Learning Networks Reprinted from: Entropy 2018, 20, 380, doi:10.3390/e20050380 ..................... 60 Alexey E. Rastegin Entropic Uncertainty Relations for Successive Measurements in the Presence of a Minimal Length Reprinted from: Entropy 2018, 20, 354, doi:10.3390/e20050354 ..................... 87 Ciann-Dong Yang and Chung-Hsuan Kuo Quantization and Bifurcation beyond Square-Integrable Wavefunctions Reprinted from: Entropy 2018, 20, 327, doi:10.3390/e20050327 .....................102 Francisco De Zela Gudder’s Theorem and the Born Rule Reprinted from: Entropy 2018, 20, 158, doi:10.3390/e20030158 .....................124 Jun Li and Shao-Ming Fei Uncertainty Relation Based on Wigner–Yanase–Dyson Skew Information with Quantum Memory Reprinted from: Entropy 2018, 20, 132, doi:10.3390/e20020132 .....................134 Fabricio Toscano, Daniel S. Tasca, Łukasz Rudnicki and Stephen P. Walborn Uncertainty Relations for Coarse–Grained Measurements: An Overview Reprinted from: Entropy 2018, 20, 454, doi:10.3390/e20060454 .....................143 v About the Special Issue Editors Pedro W. Lamberti, PhD: Dr Pedro Lamberti is a Full Professor of Theoretical Physics in the Faculty of Mathematics, Astronomy, Physics and Computation at The National University of Cordoba´ in Argentina. He is also a member of the National Council of Science and Technology (CONICET, Argentina). His research focuses on studying the definition of quantum correlations by using the notion of distances between quantum states. He also studies the dynamical properties of time series by using information theory tools. He obtained a PhD in Physics in the area of General Relativity Theory from the National University of Cordoba´ (in 1990). Gustavo M. Bosyk, PhD: Dr Gustavo Bosyk has been a Researcher at Instituto de F´ısica La Plata—CONICET (Argentina) since 2016. He studied Physics at the University of Buenos Aires (diploma awarded in 2010). He received his PhD in Physics (in 2014) from Universidad Nacional de La Plata (Argentina). His scientific interests focus on the broad field of quantum information and quantum foundations, with a particular focus on entanglement theory, quantum correlations, uncertainty relations, quantum coding, quantum resource theories, information theoretic measures, and majorization. He is the author of more than 20 peer-reviewed publications on these topics and he has participated in several international workshops and conferences on the field. Sebastian Fortin, PhD: Dr Sebastian Fortin has a degree in Physics from the University of Buenos Aires and a PhD in Epistemology and History of Science from the National University of Tres de Febrero (Argentina). He is an Assistant Researcher at CONICET and a First-Class Professor Assistant at the Physics Department of the Faculty of Exact and Natural Sciences at the University of Buenos Aires. He specializes in the philosophy of physics, particularly quantum mechanics. His research focuses on studying the classical limit based on the decoherence phenomena, quantum information, interpretation of quantum mechanics, the modal-Hamiltonian interpretation, nonunitary evolutions, irreversibility, and quantum logic. Federico Holik, PhD: Dr Federico Holik is a Research Fellow of the National Scientific and Technical Research Council in Argentina. Dr Holik studied at the University of Buenos Aires (Argentina) and held postdoctoral positions at Instituto de F´ısica La Plata (Argentina) and Universite´ Paris Diderot (France). His research focuses on quantum information theory, the foundations of quantum mechanics, the interpretation of quantum probabilities, and the study of the logical, algebraic, and geometrical aspects of the quantum formalism. vii entropy Editorial Special Issue “Quantum Foundations: 90 Years of Uncertainty” ∗ Gustavo M. Bosyk 1, Sebastian Fortin 2, Pedro W. Lamberti 3 and Federico Holik 1, 1 Instituto de Física La Plata , UNLP, CONICET, Facultad de Ciencias Exactas, 1900 La Plata, Argentina; [email protected] 2 CONICET, Departamento de Física, Universidad de Buenos Aires, Buenos Aires, C1053 CABA, Argentina; [email protected] 3 Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba & CONICET, Córdoba, Argentina; [email protected] * Correspondence: holik@fisica.unlp.edu.ar or [email protected] Received: 2 February 2019; Accepted: 6 February 2019; Published: 8 February 2019 Keywords: foundations of quantum mechanics; uncertainty relations; bell inequalities; entropy; quantum computing The VII Conference on Quantum Foundations: 90 years of uncertainty was held during November 29th to December 1st, in 2017, at the Facultad de Matemática, Astronomía, Física y Computación, Córdoba, Argentina. It gathered experts in the foundations of quantum mechanics from different countries around the world, interested in promoting a multidisciplinary approach to the fundamental questions of quantum theory and its applications, by taking in consideration not only the physical, but also the philosophical and mathematical aspects of the theory. By those days, 90 years had passed since the seminal paper of Werner Heisenberg [1], describing the reciprocal uncertainty relation between position and momentum in the quantum realm. But the intriguing questions about the interpretation of those relations in connection to the general problems of the interpretation of the quantum formalism, still remain. This was reflected in the vivid discussions that were posed during the Conference. This special issue captures the main aspects of this debate in connection with other fundamental questions of quantum theory and its applications, by incorporating a selected list of contributions that we now present below. In the paper “Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations”, by Andrei Y. Khrennikov and Elena R. Loubenets [2], a general class of symmetric two-qubit states with perfect correlations or anticorrelations between Alice and Bob was introduced. It was proved that, for all states belonging to this class, the maximal 3 violation of the original Bell inequality is upper bounded by a factor 2 and the two-qubit states where this quantum upper bound is attained were given. This is a step forward for solving the problem of finding the quantum upper bound for the original Bell inequality. The experimental implications of these results were also discussed. In the paper “Revisiting Entanglement within the Bohmian Approach to Quantum Mechanics”, by Claudia Zander and Angel Ricardo Plastino [3], the concept of entanglement was discussed in the framework of the Bohmian approach to quantum mechanics.
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