DOCSLIB.ORG

Quantum Nonlocality

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

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. 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 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
Recommended publications
  • Arxiv:1206.1084V3 [Quant-Ph] 3 May 2019

    Arxiv:1206.1084V3 [Quant-Ph] 3 May 2019

    Overview of Bohmian Mechanics Xavier Oriolsa and Jordi Mompartb∗ aDepartament d'Enginyeria Electr`onica, Universitat Aut`onomade Barcelona, 08193, Bellaterra, SPAIN bDepartament de F´ısica, Universitat Aut`onomade Barcelona, 08193 Bellaterra, SPAIN This chapter provides a fully comprehensive overview of the Bohmian formulation of quantum phenomena. It starts with a historical review of the difficulties found by Louis de Broglie, David Bohm and John Bell to convince the scientific community about the validity and utility of Bohmian mechanics. Then, a formal explanation of Bohmian mechanics for non-relativistic single-particle quantum systems is presented. The generalization to many-particle systems, where correlations play an important role, is also explained. After that, the measurement process in Bohmian mechanics is discussed. It is emphasized that Bohmian mechanics exactly reproduces the mean value and temporal and spatial correlations obtained from the standard, i.e., `orthodox', formulation. The ontological characteristics of the Bohmian theory provide a description of measurements in a natural way, without the need of introducing stochastic operators for the wavefunction collapse. Several solved problems are presented at the end of the chapter giving additional mathematical support to some particular issues. A detailed description of computational algorithms to obtain Bohmian trajectories from the numerical solution of the Schr¨odingeror the Hamilton{Jacobi equations are presented in an appendix. The motivation of this chapter is twofold.
  • Arxiv:1911.07386V2 [Quant-Ph] 25 Nov 2019

    Arxiv:1911.07386V2 [Quant-Ph] 25 Nov 2019

    Ideas Abandoned en Route to QBism Blake C. Stacey1 1Physics Department, University of Massachusetts Boston (Dated: November 26, 2019) The interpretation of quantum mechanics known as QBism developed out of efforts to understand the probabilities arising in quantum physics as Bayesian in character. But this development was neither easy nor without casualties. Many ideas voiced, and even committed to print, during earlier stages of Quantum Bayesianism turn out to be quite fallacious when seen from the vantage point of QBism. If the profession of science history needed a motto, a good candidate would be, “I think you’ll find it’s a bit more complicated than that.” This essay explores a particular application of that catechism, in the generally inconclusive and dubiously reputable area known as quantum foundations. QBism is a research program that can briefly be defined as an interpretation of quantum mechanics in which the ideas of agent and ex- perience are fundamental. A “quantum measurement” is an act that an agent performs on the external world. A “quantum state” is an agent’s encoding of her own personal expectations for what she might experience as a consequence of her actions. Moreover, each measurement outcome is a personal event, an expe- rience specific to the agent who incites it. Subjective judgments thus comprise much of the quantum machinery, but the formalism of the theory establishes the standard to which agents should strive to hold their expectations, and that standard for the relations among beliefs is as objective as any other physical theory [1]. The first use of the term QBism itself in the literature was by Fuchs and Schack in June 2009 [2].
  • Bell's Theorem and Its Tests

    Bell's Theorem and Its Tests

    PHYSICS ESSAYS 33, 2 (2020) Bell’s theorem and its tests: Proof that nature is superdeterministic—Not random Johan Hanssona) Division of Physics, Lulea˚ University of Technology, SE-971 87 Lulea˚, Sweden (Received 9 March 2020; accepted 7 May 2020; published online 22 May 2020) Abstract: By analyzing the same Bell experiment in different reference frames, we show that nature at its fundamental level is superdeterministic, not random, in contrast to what is indicated by orthodox quantum mechanics. Events—including the results of quantum mechanical measurements—in global space-time are fixed prior to measurement. VC 2020 Physics Essays Publication. [http://dx.doi.org/10.4006/0836-1398-33.2.216] Resume: En analysant l’experience de Bell dans d’autres cadres de reference, nous demontrons que la nature est super deterministe au niveau fondamental et non pas aleatoire, contrairement ace que predit la mecanique quantique. Des evenements, incluant les resultats des mesures mecaniques quantiques, dans un espace-temps global sont fixes avant la mesure. Key words: Quantum Nonlocality; Bell’s Theorem; Quantum Measurement. Bell’s theorem1 is not merely a statement about quantum Registered outcomes at either side, however, are classi- mechanics but about nature itself, and will survive even if cal objective events (for example, a sequence of zeros and quantum mechanics is superseded by an even more funda- ones representing spin up or down along some chosen mental theory in the future. Although Bell used aspects of direction), e.g., markings on a paper printout ¼ classical quantum theory in his original proof, the same results can be facts ¼ events ¼ points defining (constituting) global space- obtained without doing so.2,3 The many experimental tests of time itself.
  • Arxiv:1607.01025V2

    Arxiv:1607.01025V2

    Observables, gravitational dressing, and obstructions to locality and subsystems William Donnelly∗ and Steven B. Giddings† Department of Physics, University of California, Santa Barbara, CA 93106 Quantum field theory – our basic framework for describing all nongravitational physics – conflicts with general relativity: the latter precludes the standard definition of the former’s essential principle of locality, in terms of commuting local observables. We examine this conflict more carefully, by investigating implications of gauge (diffeomorphism) invariance for observables in gravity. We prove a dressing theorem, showing that any operator with nonzero Poincar´echarges, and in particular any compactly supported operator, in flat-spacetime quantum field theory must be gravitationally dressed once coupled to gravity, i.e. it must depend on the metric at arbitrarily long distances, and we put lower bounds on this nonlocal dependence. This departure from standard locality occurs in the most severe way possible: in perturbation theory about flat spacetime, at leading order in Newton’s constant. The physical observables in a gravitational theory therefore do not organize themselves into local commuting subalgebras: the principle of locality must apparently be reformulated or abandoned, and in fact we lack a clear definition of the coarser and more basic notion of a quantum subsystem of the Universe. We discuss relational approaches to locality based on diffeomorphism-invariant nonlocal operators, and reinforce arguments that any such locality is state-dependent and approximate. We also find limitations to the utility of bilocal diffeomorphism- invariant operators that are considered in cosmological contexts. An appendix provides a concise review of the canonical covariant formalism for gravity, instrumental in the discussion of Poincar´e charges and their associated long-range fields.
  • A Non-Technical Explanation of the Bell Inequality Eliminated by EPR Analysis Eliminated by Bell A

    A Non-Technical Explanation of the Bell Inequality Eliminated by EPR Analysis Eliminated by Bell A

    Ghostly action at a distance: a non-technical explanation of the Bell inequality Mark G. Alford Physics Department, Washington University, Saint Louis, MO 63130, USA (Dated: 16 Jan 2016) We give a simple non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality, also known as local causality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism. I. INTRODUCTION II. OVERVIEW To make it clear how EPR experiments falsify the prin- The recent announcement of a \loophole-free" observa- ciple of strong locality, we now give an overview of the tion of violation of the Bell inequality [1] has brought re- logical context (Fig. 1). For pedagogical purposes it is newed attention to the Einstein-Podolsky-Rosen (EPR) natural to present the analysis of the experimental re- family of experiments in which such violation is observed. sults in two stages, which we will call the \EPR analy- The violation of the Bell inequality is often described as sis", and the \Bell analysis" although historically they falsifying the combination of \locality" and \realism". were not presented in exactly this form [4, 5]; indeed, However, we will follow the approach of other authors both stages are combined in Bell's 1976 paper [2]. including Bell [2{4] who emphasize that the EPR results We will concentrate on Bohm's variant of EPR, the violate a single principle, strong locality.
  • Arxiv:2002.00255V3 [Quant-Ph] 13 Feb 2021 Lem (BVP)

    Arxiv:2002.00255V3 [Quant-Ph] 13 Feb 2021 Lem (BVP)

    A Path Integral approach to Quantum Fluid Dynamics Sagnik Ghosh Indian Institute of Science Education and Research, Pune-411008, India Swapan K Ghosh UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Kalina, Santacruz, Mumbai-400098, India ∗ (Dated: February 16, 2021) In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs) simultaneously. We opt for a fundamentally different route. We first derive a general closed form expression for the Path Integral propagator valid for any general potential as a functional of the corresponding classical path. The method is exact and is applicable in many dimensions as well as multi-particle cases. This, then, is used to compute the Quantum Potential (QP), which, in turn, can generate the Quantum Trajectories. For cases, where closed form solution is not possible, the problem is formally boiled down to solving the classical path as a boundary value problem. The work formally bridges the Path Integral approach with Quantum Fluid Dynamics. As a model application to illustrate the method, we work out a toy model viz. the double-well potential, where the boundary value problem for the classical path has been computed perturbatively, but the Quantum part is left exact. Using this we delve into seeking insight in one of the long standing debates with regard to Quantum Tunneling. Keywords: Path Integral, Quantum Fluid Dynamics, Analytical Solution, Quantum Potential, Quantum Tunneling, Quantum Trajectories Submitted to: J.
  • Optomechanical Bell Test

    Optomechanical Bell Test

    Delft University of Technology Optomechanical Bell Test Marinković, Igor; Wallucks, Andreas; Riedinger, Ralf; Hong, Sungkun; Aspelmeyer, Markus; Gröblacher, Simon DOI 10.1103/PhysRevLett.121.220404 Publication date 2018 Document Version Final published version Published in Physical Review Letters Citation (APA) Marinković, I., Wallucks, A., Riedinger, R., Hong, S., Aspelmeyer, M., & Gröblacher, S. (2018). Optomechanical Bell Test. Physical Review Letters, 121(22), [220404]. https://doi.org/10.1103/PhysRevLett.121.220404 Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10. PHYSICAL REVIEW LETTERS 121, 220404 (2018) Editors' Suggestion Featured in Physics Optomechanical Bell Test † Igor Marinković,1,* Andreas Wallucks,1,* Ralf Riedinger,2 Sungkun Hong,2 Markus Aspelmeyer,2 and Simon Gröblacher1, 1Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628CJ Delft, Netherlands 2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria (Received 18 June 2018; published 29 November 2018) Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications.
  • A Practical Phase Gate for Producing Bell Violations in Majorana Wires

    A Practical Phase Gate for Producing Bell Violations in Majorana Wires

    PHYSICAL REVIEW X 6, 021005 (2016) A Practical Phase Gate for Producing Bell Violations in Majorana Wires David J. Clarke, Jay D. Sau, and Sankar Das Sarma Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA (Received 9 October 2015; published 8 April 2016) Carrying out fault-tolerant topological quantum computation using non-Abelian anyons (e.g., Majorana zero modes) is currently an important goal of worldwide experimental efforts. However, the Gottesman- Knill theorem [1] holds that if a system can only perform a certain subset of available quantum operations (i.e., operations from the Clifford group) in addition to the preparation and detection of qubit states in the computational basis, then that system is insufficient for universal quantum computation. Indeed, any measurement results in such a system could be reproduced within a local hidden variable theory, so there is no need for a quantum-mechanical explanation and therefore no possibility of quantum speedup [2]. Unfortunately, Clifford operations are precisely the ones available through braiding and measurement in systems supporting non-Abelian Majorana zero modes, which are otherwise an excellent candidate for topologically protected quantum computation. In order to move beyond the classically simulable subspace, an additional phase gate is required. This phase gate allows the system to violate the Bell-like Clauser- Horne-Shimony-Holt (CHSH) inequality that would constrain a local hidden variable theory. In this article, we introduce a new type of phase gate for the already-existing semiconductor-based Majorana wire systems and demonstrate how this phase gate may be benchmarked using CHSH measurements.
  • Physics of Information in Nonequilibrium Systems A

    Physics of Information in Nonequilibrium Systems A

    PHYSICS OF INFORMATION IN NONEQUILIBRIUM SYSTEMS A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HAWAI`I AT MANOA¯ IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS MAY 2019 By Elan Stopnitzky Thesis Committee: Susanne Still, Chairperson Jason Kumar Yuriy Mileyko Xerxes Tata Jeffrey Yepez Copyright c 2019 by Elan Stopnitzky ii To my late grandmother, Rosa Stopnitzky iii ACKNOWLEDGMENTS I thank my wonderful family members Benny, Patrick, Shanee, Windy, and Yaniv for the limitless love and inspiration they have given to me over the years. I thank as well my advisor Susanna Still, who has always put great faith in me and encouraged me to pursue my own research ideas, and who has contributed to this work and influenced me greatly as a scientist; my friend and collaborator Lee Altenberg, whom I have learned countless things from and who contributed significantly to this thesis; and my collaborator Thomas E. Ouldridge, who also made important contributions. Finally, I would like to thank my partner Danelle Gallo, whose kindness and support have been invaluable to me throughout this process. iv ABSTRACT Recent advances in non-equilibrium thermodynamics have begun to reveal the funda- mental physical costs, benefits, and limits to the use of information. As the processing of information is a central feature of biology and human civilization, this opens the door to a physical understanding of a wide range of complex phenomena. I discuss two areas where connections between non-equilibrium physics and information theory lead to new results: inferring the distribution of biologically important molecules on the abiotic early Earth, and the conversion of correlated bits into work.
  • Pilot-Wave Theory, Bohmian Metaphysics, and the Foundations of Quantum Mechanics Lecture 6 Calculating Things with Quantum Trajectories

    Pilot-Wave Theory, Bohmian Metaphysics, and the Foundations of Quantum Mechanics Lecture 6 Calculating Things with Quantum Trajectories

    Pilot-wave theory, Bohmian metaphysics, and the foundations of quantum mechanics Lecture 6 Calculating things with quantum trajectories Mike Towler TCM Group, Cavendish Laboratory, University of Cambridge www.tcm.phy.cam.ac.uk/∼mdt26 and www.vallico.net/tti/tti.html [email protected] – Typeset by FoilTEX – 1 Acknowledgements The material in this lecture is to a large extent a summary of publications by Peter Holland, R.E. Wyatt, D.A. Deckert, R. Tumulka, D.J. Tannor, D. Bohm, B.J. Hiley, I.P. Christov and J.D. Watson. Other sources used and many other interesting papers are listed on the course web page: www.tcm.phy.cam.ac.uk/∼mdt26/pilot waves.html MDT – Typeset by FoilTEX – 2 On anticlimaxes.. Up to now we have enjoyed ourselves freewheeling through the highs and lows of fundamental quantum and relativistic physics whilst slagging off Bohr, Heisenberg, Pauli, Wheeler, Oppenheimer, Born, Feynman and other physics heroes (last week we even disagreed with Einstein - an attitude that since the dawn of the 20th century has been the ultimate sign of gibbering insanity). All tremendous fun. This week - we shall learn about finite differencing and least squares fitting..! Cough. “Dr. Towler, please. You’re not allowed to use the sprinkler system to keep the audience awake.” – Typeset by FoilTEX – 3 QM computations with trajectories Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation P. Holland (2004) “The notion that the concept of a continuous material orbit is incompatible with a full wave theory of microphysical systems was central to the genesis of wave mechanics.
  • Quantum Aspects of Life / Editors, Derek Abbott, Paul C.W

    Quantum Aspects of Life / Editors, Derek Abbott, Paul C.W

    Quantum Aspectsof Life P581tp.indd 1 8/18/08 8:42:58 AM This page intentionally left blank foreword by SIR ROGER PENROSE editors Derek Abbott (University of Adelaide, Australia) Paul C. W. Davies (Arizona State University, USAU Arun K. Pati (Institute of Physics, Orissa, India) Imperial College Press ICP P581tp.indd 2 8/18/08 8:42:58 AM Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Quantum aspects of life / editors, Derek Abbott, Paul C.W. Davies, Arun K. Pati ; foreword by Sir Roger Penrose. p. ; cm. Includes bibliographical references and index. ISBN-13: 978-1-84816-253-2 (hardcover : alk. paper) ISBN-10: 1-84816-253-7 (hardcover : alk. paper) ISBN-13: 978-1-84816-267-9 (pbk. : alk. paper) ISBN-10: 1-84816-267-7 (pbk. : alk. paper) 1. Quantum biochemistry. I. Abbott, Derek, 1960– II. Davies, P. C. W. III. Pati, Arun K. [DNLM: 1. Biogenesis. 2. Quantum Theory. 3. Evolution, Molecular. QH 325 Q15 2008] QP517.Q34.Q36 2008 576.8'3--dc22 2008029345 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Photo credit: Abigail P. Abbott for the photo on cover and title page. Copyright © 2008 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
  • Simulation of the Bell Inequality Violation Based on Quantum Steering Concept Mohsen Ruzbehani

    Simulation of the Bell Inequality Violation Based on Quantum Steering Concept Mohsen Ruzbehani

    www.nature.com/scientificreports OPEN Simulation of the Bell inequality violation based on quantum steering concept Mohsen Ruzbehani Violation of Bell’s inequality in experiments shows that predictions of local realistic models disagree with those of quantum mechanics. However, despite the quantum mechanics formalism, there are debates on how does it happen in nature. In this paper by use of a model of polarizers that obeys the Malus’ law and quantum steering concept, i.e. superluminal infuence of the states of entangled pairs to each other, simulation of phenomena is presented. The given model, as it is intended to be, is extremely simple without using mathematical formalism of quantum mechanics. However, the result completely agrees with prediction of quantum mechanics. Although it may seem trivial, this model can be applied to simulate the behavior of other not easy to analytically evaluate efects, such as defciency of detectors and polarizers, diferent value of photons in each run and so on. For example, it is demonstrated, when detector efciency is 83% the S factor of CHSH inequality will be 2, which completely agrees with famous detector efciency limit calculated analytically. Also, it is shown in one-channel polarizers the polarization of absorbed photons, should change to the perpendicular of polarizer angle, at very end, to have perfect violation of the Bell inequality (2 √2 ) otherwise maximum violation will be limited to (1.5 √2). More than a half-century afer celebrated Bell inequality 1, nonlocality is almost totally accepted concept which has been proved by numerous experiments. Although there is no doubt about validity of the mathematical model proposed by Bell to examine the principle of the locality, it is comprehended that Bell’s inequality in its original form is not testable.