DOCSLIB.ORG

The Case for Quantum State Realism

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Case for Quantum State Realism Western University Scholarship@Western Electronic Thesis and Dissertation Repository 4-23-2012 12:00 AM The Case for Quantum State Realism Morgan C. Tait The University of Western Ontario Supervisor Wayne Myrvold The University of Western Ontario Graduate Program in Philosophy A thesis submitted in partial fulfillment of the equirr ements for the degree in Doctor of Philosophy © Morgan C. Tait 2012 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Philosophy Commons Recommended Citation Tait, Morgan C., "The Case for Quantum State Realism" (2012). Electronic Thesis and Dissertation Repository. 499. https://ir.lib.uwo.ca/etd/499 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. THE CASE FOR QUANTUM STATE REALISM Thesis format: Monograph by Morgan Tait Department of Philosophy A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy The School of Graduate and Postdoctoral Studies The University of Western Ontario London, Ontario, Canada © Morgan Tait 2012 THE UNIVERSITY OF WESTERN ONTARIO School of Graduate and Postdoctoral Studies CERTIFICATE OF EXAMINATION Supervisor Examiners ______________________________ ______________________________ Dr. Wayne Myrvold Dr. Dan Christensen Supervisory Committee ______________________________ Dr. Robert Spekkens ______________________________ Dr. Robert DiSalle ______________________________ Dr. Chris Smeenk The thesis by Morgan Christopher Tait entitled: The Case for Quantum State Realism is accepted in partial fulfillment of the requirements for the degree of « Doctor of Philosophy» ______________________ _______________________________ Date Chair of the Thesis Examination Board ii Abstract I argue for a realist interpretation of the quantum state. I begin by reviewing and critically evaluating two arguments for an antirealist interpretation of the quantum state, the first derived from the so-called ‘measurement problem’, and the second from the concept of local causality. I argue that existing antirealist interpretations do not solve the measurement problem. Furthermore, I argue that it is possible to construct a local, realist interpretation of quantum mechanics, using methods borrowed from quantum field theory and based on John S. Bell’s concept of ‘local beables’. If the quantum state is interpreted subjectively, then the probabilities it associates with experimental outcomes are themselves subjective. I address the prospects for developing a subjective Bayesian interpretation of quantum mechanical probabilities based on the Quantum de Finetti Representation Theorem. Epistemic interpretations of the quantum state can be divided into those that are epistemic with respect to underlying ontic states, and those that are epistemic with respect to measurement outcomes. The Pusey Barrett and Rudolph (PBR) theorem places serious constraints on the former family of interpretations. I identify an important explanatory gap in the latter sort of interpretation. In particular, if the quantum state is a subjective representation of beliefs about future experimental outcomes, then it is not clear why those experimenters who use quantum mechanics should be better able to negotiate the world than those who do not. iii I then turn to the task of articulating a positive argument for the thesis of quantum state realism. I begin by articulating a minimal set of conditions that any realist interpretation must meet. One assumption built into the PBR result is that systems prepared in a given quantum state have a well-defined set of physical properties, which may be completely or incompletely described by the quantum state. Antirealist interpretations that reject this assumption are therefore compatible with the PBR result. A compelling case for quantum state realism must therefore be made on more general grounds. I consider two concrete examples of phenomena described by quantum mechanics that strongly suggest that the quantum state is genuinely representational in character. Keywords: Philosophy of physics, foundations of quantum mechanics, the measurement problem, philosophy of science, quantum state, realism, confirmation theory, philosophy of probability iv For Rick Tait and Meaghan Eastwood v Acknowledgements I would like to extend a very special thank you to Wayne Myrvold. This project would not have been possible without Wayne’s constant intellectual support and encouragement. Special thanks to Robert DiSalle, Chris Smeenk, William Demopoulos and Erik Curiel for valuable discussion and comments along the way. Thank you also to Ryan Samaroo, Mike Cuffaro, Molly Kao, Robert Batterman, William Harper, and Doreen Fraser. I would also like to thank my external examiners Robert Spekkens and Dan Christensen. I owe a special debt of gratitude to Chris Fuchs, whose work in the foundations of quantum mechanics was an inspiration for this project, and who very graciously invited me to participate in discussions at the Perimeter Institute for Theoretical Physics in the fall of 2009. Finally, I would like to gratefully acknowledge financial support from the Social Sciences and Humanities Research Council and the Foundational Questions Institute. vi Table of Contents Certificate of Examination ................................................................................................................... ii Abstract ......................................................................................................................................................iii Acknowledgements ............................................................................................................................... vi Table of Contents ................................................................................................................................. vii Introduction .............................................................................................................................................. 1 Why Does Quantum Mechanics Need an Interpretation? .................................................. 1 Motivations for Quantum State Antirealism ............................................................................ 4 Outline of Thesis Structure ............................................................................................................. 9 Chapter 2: Critical Examination of Two Arguments for Quantum State Antirealism 14 Introduction ...................................................................................................................................... 14 2.1 The Measurement Problem as Motivation for Quantum State Antirealism ...... 21 Bub on the ‘Two Dogmas of Quantum Mechanics’ ........................................................ 24 Fuchs on Quantum Measurement as Bayesian Updating............................................ 35 2.2 Is Locality Incompatible with Quantum State Realism? ...................................... 47 Einstein’s Incompleteness argument and Quantum State Antirealism ................. 47 The Bell Factorizability Condition and Locality ............................................................. 52 Local Beables and the Prospects for a Local, Realist Quantum Theory ................ 62 Conclusion .......................................................................................................................................... 72 Chapter 3: Evidence, Explanation and the Quantum State .................................................. 74 Introduction: The Nature of Probabilities, Classical and Quantum ............................. 74 The Dualistic Conception of Probability ............................................................................ 74 The Subjectivist Interpretation of Probability and Quantum State Tomography ........................................................................................................................................................... 79 vii 3.1 The Subjectivist Interpretation of Probability and Quantum Bayesianism ...... 83 Quantum Bayesianism and the Space of Epistemic Interpretations of the Quantum State ............................................................................................................................. 84 The de Finetti Representation Theorem ........................................................................... 89 The Quantum de Finetti Representation Theorem and Quantum State Tomography ................................................................................................................................. 96 3.2 The Means/Ends Objection and the Role of the Preparation Device ................. 101 The Born Rule as an Empirical Addition to Bayesian Coherence .......................... 115 Conclusion ........................................................................................................................................ 128 Chapter 4: The Case for Quantum State Realism ................................................................... 130 Introduction .................................................................................................................................... 130 4.1 Yes, but… .............................................................................................................................
Load more

Recommended publications
  • Arxiv:2004.01992V2 [Quant-Ph] 31 Jan 2021 Ity [6–20]
    Hidden Variable Model for Universal Quantum Computation with Magic States on Qubits Michael Zurel,1, 2, ∗ Cihan Okay,1, 2, ∗ and Robert Raussendorf1, 2 1Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada 2Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada (Dated: February 2, 2021) We show that every quantum computation can be described by a probabilistic update of a proba- bility distribution on a finite phase space. Negativity in a quasiprobability function is not required in states or operations. Our result is consistent with Gleason's Theorem and the Pusey-Barrett- Rudolph theorem. It is often pointed out that the fundamental objects In Theorem 2, we apply this to quantum computation in quantum mechanics are amplitudes, not probabilities with magic states, showing that universal quantum com- [1, 2]. This fact notwithstanding, here we construct a de- putation can be classically simulated by the probabilistic scription of universal quantum computation|and hence update of a probability distribution. of all quantum mechanics in finite-dimensional Hilbert This looks all very classical, and therein lies a puzzle. spaces|in terms of a probabilistic update of a probabil- In fact, our Theorem 2 is running up against a number ity distribution. In this formulation, quantum algorithms of no-go theorems: Theorem 2 in [23] and the Pusey- look structurally akin to classical diffusion problems. Barrett-Rudolph (PBR) theorem [24] say that probabil- While this seems implausible, there exists a well-known ity representations for quantum mechanics do not exist, special instance of it: quantum computation with magic and [9{13] show that negativity in certain Wigner func- states (QCM) [3] on a single qubit.
    [Show full text]
  • Arxiv:1909.06771V2 [Quant-Ph] 19 Sep 2019
    Quantum PBR Theorem as a Monty Hall Game Del Rajan ID and Matt Visser ID School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand. (Dated: LATEX-ed September 20, 2019) The quantum Pusey{Barrett{Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a -ontic model (system's physical state) or to a -epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a -ontic or -epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability. Introduction: No-go theorems in quantum foundations Furthermore, concepts involved in the PBR proof have are vitally important for our understanding of quantum been used for a particular guessing game [43]. physics. Bell's theorem [1] exemplifies this by showing In this Letter, we reformulate the PBR theorem into that locally realistic models must contradict the experi- a Monty Hall game. This particular gamification of the mental predictions of quantum theory. theorem highlights that winning probabilities, for switch- There are various ways of viewing Bell's theorem ing doors in the game, depend on whether it is a -ontic through the framework of game theory [2]. These are or -epistemic game; we also show that in certain - commonly referred to as nonlocal games, and the best epistemic games switching doors provides no advantage. known example is the CHSH game; in this scenario the This may have consequences for an alternative experi- participants can win the game at a higher probability mental test of the PBR theorem.
    [Show full text]
  • The Mathemathics of Secrets.Pdf
    THE MATHEMATICS OF SECRETS THE MATHEMATICS OF SECRETS CRYPTOGRAPHY FROM CAESAR CIPHERS TO DIGITAL ENCRYPTION JOSHUA HOLDEN PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c 2017 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket image courtesy of Shutterstock; design by Lorraine Betz Doneker All Rights Reserved Library of Congress Cataloging-in-Publication Data Names: Holden, Joshua, 1970– author. Title: The mathematics of secrets : cryptography from Caesar ciphers to digital encryption / Joshua Holden. Description: Princeton : Princeton University Press, [2017] | Includes bibliographical references and index. Identifiers: LCCN 2016014840 | ISBN 9780691141756 (hardcover : alk. paper) Subjects: LCSH: Cryptography—Mathematics. | Ciphers. | Computer security. Classification: LCC Z103 .H664 2017 | DDC 005.8/2—dc23 LC record available at https://lccn.loc.gov/2016014840 British Library Cataloging-in-Publication Data is available This book has been composed in Linux Libertine Printed on acid-free paper. ∞ Printed in the United States of America 13579108642 To Lana and Richard for their love and support CONTENTS Preface xi Acknowledgments xiii Introduction to Ciphers and Substitution 1 1.1 Alice and Bob and Carl and Julius: Terminology and Caesar Cipher 1 1.2 The Key to the Matter: Generalizing the Caesar Cipher 4 1.3 Multiplicative Ciphers 6
    [Show full text]
  • Reformulation of Quantum Mechanics and Strong Complementarity from Bayesian Inference Requirements
    Reformulation of quantum mechanics and strong complementarity from Bayesian inference requirements William Heartspring Abstract: This paper provides an epistemic reformulation of quantum mechanics (QM) in terms of inference consistency requirements of objective Bayesianism, which include the principle of maximum entropy under physical constraints. Physical constraints themselves are understood in terms of consistency requirements. The by-product of this approach is that QM must additionally be understood as providing the theory of theories. Strong complementarity - that dierent observers may live in separate Hilbert spaces - follows as a consequence, which resolves the rewall paradox. Other clues pointing to this reformu- lation are analyzed. The reformulation, with the addition of novel transition probability arithmetic, resolves the measurement problem completely, thereby eliminating subjectivity of measurements from quantum mechanics. An illusion of collapse comes from Bayesian updates by observer's continuous outcome data. Dark matter and dark energy pop up directly as entropic tug-of-war in the reformulation. Contents 1 Introduction1 2 Epistemic nature of quantum mechanics2 2.1 Area law, quantum information and spacetime2 2.2 State vector from objective Bayesianism5 3 Consequences of the QM reformulation8 3.1 Basis, decoherence and causal diamond complementarity 12 4 Spacetime from entanglement 14 4.1 Locality: area equals mutual information 14 4.2 Story of Big Bang cosmology 14 5 Evidences toward the reformulation 14 5.1 Quantum redundancy 15 6 Transition probability arithmetic: resolving the measurement problem completely 16 7 Conclusion 17 1 Introduction Hamiltonian formalism and Schrödinger picture of quantum mechanics are assumed through- out the writing, with time t 2 R. Whenever the word entropy is mentioned without addi- tional qualication, it refers to von Neumann entropy.
    [Show full text]
  • Antum Entanglement in Time
    antum Entanglement in Time by Del Rajan A thesis submied to the Victoria University of Wellington in fullment of the requirements for the degree of Doctor of Philosophy Victoria University of Wellington 2020 Abstract is thesis is in the eld of quantum information science, which is an area that reconceptualizes quantum physics in terms of information. Central to this area is the quantum eect of entanglement in space. It is an interdependence among two or more spatially separated quantum systems that would be impossible to replicate by classical systems. Alternatively, an entanglement in space can also be viewed as a resource in quantum information in that it allows the ability to perform information tasks that would be impossible or very dicult to do with only classical information. Two such astonishing applications are quantum com- munications which can be harnessed for teleportation, and quantum computers which can drastically outperform the best classical supercomputers. In this thesis our focus is on the theoretical aspect of the eld, and we provide one of the rst expositions on an analogous quantum eect known as entanglement in time. It can be viewed as an interdependence of quantum systems across time, which is stronger than could ever exist between classical systems. We explore this temporal eect within the study of quantum information and its foundations as well as through relativistic quantum information. An original contribution of this thesis is the design of one of the rst quantum information applications of entanglement in time, namely a quantum blockchain. We describe how the entanglement in time provides the quantum advantage over a classical blockchain.
    [Show full text]
  • Quantum PBR Theorem As a Monty Hall Game
    quantum reports Article Quantum PBR Theorem as a Monty Hall Game Del Rajan * and Matt Visser School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand; [email protected] * Correspondence: [email protected] Received: 21 November 2019; Accepted: 27 December 2019; Published: 31 December 2019 Abstract: The quantum Pusey–Barrett–Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a y-ontic model (system’s physical state) or to a y-epistemic model (observer’s knowledge about the system). We reformulate the PBR theorem as a Monty Hall game and show that winning probabilities, for switching doors in the game, depend on whether it is a y-ontic or y-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved in quantum teleportation, in particular for improving reliability. Keywords: Monty Hall game; PBR theorem; entanglement; teleportation; psi-ontic; psi-epistemic PACS: 03.67.Bg; 03.67.Dd; 03.67.Hk; 03.67.Mn 1. Introduction No-go theorems in quantum foundations are vitally important for our understanding of quantum physics. Bell’s theorem [1] exemplifies this by showing that locally realistic models must contradict the experimental predictions of quantum theory. There are various ways of viewing Bell’s theorem through the framework of game theory [2]. These are commonly referred to as nonlocal games, and the best known example is the CHSHgame; in this scenario, the participants can win the game at a higher probability with quantum resources, as opposed to having access to only classical resources.
    [Show full text]
  • Report of on the Reality of the Quantum State Article
    Report of On the reality of the quantum state article De´akNorbert December 6, 2016 1 Introduction Quantum states are the fundamental elements in quantum theory. How- ever, there are a lot of discussions and debates about what a quantum state actually represents. Is it corresponding directly to reality, or is it only a de- scription of what an experimenter knows of some aspect of reality, a physical system? There is a terminology to distinct the two theories: ontic state (state of reality) or epistemic state (state of knowledge). In [1], this is referred as the -ontic/epistemic distinction. The arguments started with the beginnings of quantum theory, with the debates between Bohr-Einstein, concerning the foundations of quantum me- chanics. In 1935, Einstein, Podolsky and Rosen published a paper stating that quantum mechanics is incomplete. As a repsonse, Bohr also published a paper, in which he defended the so called Copenhagen interpretation, a theory strongly supported by himself, Heisenberg and Pauli, that views the quantum state as epistemic [2]. One of the scientific works stating that the quantum state is less real is Spekken's toy theory [3]. It introduces a model, in which a toy bit as a system that can be in one of the four states: (-,-), (-,+), (+,-) and (+,+), represent- ing them on the xy plane, each of them being in a different quadrant. In this representation, the quantum states are epistemic, they are represented by probability distributions. Using this toy theory, Spekkens offers natural ex- planations for some features of quantum theory, like the non-distinguishibility of the non-orthogonal states and the no-cloning theorem.
    [Show full text]
  • The End of a Classical Ontology for Quantum Mechanics?
    entropy Article The End of a Classical Ontology for Quantum Mechanics? Peter W. Evans School of Historical and Philosophical Inquiry, University of Queensland, St Lucia, QLD 4072, Australia; [email protected] Abstract: In this paper, I argue that the Shrapnel–Costa no-go theorem undermines the last remaining viability of the view that the fundamental ontology of quantum mechanics is essentially classical: that is, the view that physical reality is underpinned by objectively real, counterfactually definite, uniquely spatiotemporally defined, local, dynamical entities with determinate valued properties, and where typically ‘quantum’ behaviour emerges as a function of our own in-principle ignorance of such entities. Call this view Einstein–Bell realism. One can show that the causally symmetric local hidden variable approach to interpreting quantum theory is the most natural interpretation that follows from Einstein–Bell realism, where causal symmetry plays a significant role in circumventing the nonclassical consequences of the traditional no-go theorems. However, Shrapnel and Costa argue that exotic causal structures, such as causal symmetry, are incapable of explaining quantum behaviour as arising as a result of noncontextual ontological properties of the world. This is partic- ularly worrying for Einstein–Bell realism and classical ontology. In the first instance, the obvious consequence of the theorem is a straightforward rejection of Einstein–Bell realism. However, more than this, I argue that, even where there looks to be a possibility of accounting for contextual ontic variables within a causally symmetric framework, the cost of such an account undermines a key advantage of causal symmetry: that accepting causal symmetry is more economical than rejecting a classical ontology.
    [Show full text]
  • The Mathematical Structure of Non-Locality & Contextuality
    The Mathematical Structure of Non-locality & Contextuality Shane Mansfield Wolfson College University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity Term 2013 To my family. Acknowledgements I would like to thank my supervisors Samson Abramsky and Bob Coecke for taking me under their wing, and for their encouragement and guidance throughout this project; my collaborators Samson Abramsky, Tobias Fritz and Rui Soares Barbosa, who have contributed to some of the work contained here; and all of the members of the Quantum Group, past and present, for providing such a stimulating and colourful environment to work in. I gratefully acknowledge financial support from the National University of Ireland Travelling Studentship programme. I'm fortunate to have many wonderful friends, who have played a huge part in making this such an enjoyable experience and who have been a great support to me. A few people deserve a special mention: Rui Soares Barbosa, who caused me to and kept me from `banging two empty halves of coconut together' at various times, and who very generously proof-read this dissertation; Daniel `The Font of all Knowledge' Corbett; Tahir Mansoori, who looked after me when I was laid up with a knee injury; mo chara dh´ılis,fear m´orna Gaeilge, Daith´ı O´ R´ıog´ain;Johan Paulsson, my companion since Part III; all of my friends at Wolfson College, you know who you are; Alina, Michael, Jon & Pernilla, Matteo; Bowsh, Matt, Lewis; Ant´on,Henry, Vincent, Joe, Ruth, the Croatians; Jerry & Joe at the lodge; the Radish, Ray; my flatmates; again, the entire Quantum Group, past and present; the Cambridge crew, Raph, Emma & Marion; Colm, Dave, Goold, Samantha, Steve, Tony and the rest of the UCC gang; the veteran Hardy Bucks, Rossi, Diarmuid & John, and the Abbeyside lads; Brendan, Cormac, and the organisers and participants of the PSM.
    [Show full text]
  • Reading List on Philosophy of Quantum Mechanics David Wallace, June 2018
    Reading list on philosophy of quantum mechanics David Wallace, June 2018 1. Introduction .............................................................................................................................................. 2 2. Introductory and general readings in philosophy of quantum theory ..................................................... 4 3. Physics and math resources ...................................................................................................................... 5 4. The quantum measurement problem....................................................................................................... 7 4. Non-locality in quantum theory ................................................................................................................ 8 5. State-eliminativist hidden variable theories (aka Psi-epistemic theories) ............................................. 10 6. The Copenhagen interpretation and its descendants ............................................................................ 12 7. Decoherence ........................................................................................................................................... 15 8. The Everett interpretation (aka the Many-Worlds Theory) .................................................................... 17 9. The de Broglie-Bohm theory ................................................................................................................... 22 10. Dynamical-collapse theories ................................................................................................................
    [Show full text]
  • Long Distance Free-Space Quantum Key Distribution
    Long distance free-space quantum key distribution Tobias Schmitt-Manderbach M¨unchen 2007 Long distance free-space quantum key distribution Tobias Schmitt-Manderbach Dissertation at the Faculty of Physics of the Ludwig–Maximilians–Universit¨at M¨unchen Tobias Schmitt-Manderbach born in M¨unchen, Germany M¨unchen, 16. Oktober 2007 Erstgutachter: Prof. Dr. Harald Weinfurter Zweitgutachter: Prof. Dr. Wolfgang Zinth Tag der m¨undlichen Pr¨ufung: 17. Dezember 2007 Zusammenfassung Im Zeitalter der Information und der Globalisierung nimmt die sichere Kommunikation und der Schutz von sensiblen Daten gegen unberechtigten Zugriff eine zentrale Stellung ein. Die Quantenkryptographie ist derzeit die einzige Methode, die den Austausch ei- nes geheimen Schl¨ussels zwischen zwei Parteien auf beweisbar sichere Weise erm¨oglicht. Mit der aktuellen Glasfaser- und Detektortechnologie ist die Quantenkrypographie auf- grund von Verlusten und Rauschen derzeit auf Entfernungen unterhalb einiger 100 km beschr¨ankt. Prinzipiell k¨onnten gr¨oßere Entfernungen in k¨urzere Abschnitte aufgeteilt werden, die daf¨ur ben¨otigten Quantenrepeater sind jedoch derzeit nicht realisierbar. Eine alternative L¨osung zur Uberwindung¨ gr¨oßerer Entfernungen stellt ein satellitenbasiertes System dar, das den Schl¨usselaustausch zwischen zwei beliebigen Punkten auf dem Glo- bus mittels freiraumoptischer Kommunikation erm¨oglichen w¨urde. Ziel des beschriebenen Experiments war es, die Realisierbarkeit satellitengest¨utzter globaler Quantenschl¨usselverteilung zu untersuchen. Dazu wurde ein freiraumoptisches Quantenkryptographie-Experimentuber ¨ eine Entfernung von 144 km durchgef¨uhrt. Sen- der und Empf¨anger befanden sich jeweils in ca. 2500 m H¨ohe auf den Kanarischen Inseln La Palma bzw. Teneriffa. Die kleine und leichte Sendeeinheit erzeugte abgeschw¨achte Laserpulse, die mittels eines 15-cm Teleskops zum Empf¨anger geschickt wurden.
    [Show full text]
  • Arxiv:1312.1345V1 [Quant-Ph] 4 Dec 2013
    The whole is greater than the sum of the parts: on the possibility of purely statistical interpretations of quantum theory Joseph Emerson, Dmitry Serbin, Chris Sutherland, Victor Veitch Institute for Quantum Computing, 200 University Ave West, Waterloo, ON, Canada (Dated: July 16, 2018) The Pusey-Barrett-Rudolph theorem (PBR) claims to rule out the possibility of a purely sta- tistical interpretation of the quantum state under an assumption of how to represent independent operations in any hidden variable model. We show that PBR's assumption of independence encodes an assumption of local causality, which is already known to conflict with the predictions of quantum theory via Bell-type inequalities. We devise a weaker formulation of independence within a general hidden variable model that is empirically indistinguishable from the PBR assumption in situations where certain hidden variables are inaccessible. Under this weaker principle we are able to construct an explicit hidden variable model that is purely statistical and also reproduces the quantum predic- tions. Our results suggest that the assumption of a purely statistical interpretation is actually an innocent bystander in the PBR argument, rather than the driving force behind their contradiction. \What is proved by the impossibility proofs inference is characterized as an implication of their result is lack of imagination."[1] [6, 7]. Because the PBR assumption of preparation in- { John S. Bell dependence involves an assumption of locality, it is this assumption that should be regarded with utmost suspi- Perhaps the most long-standing open question in the cion; readers that consider locality assumptions natural foundations of quantum mechanics is whether pure quan- in the hidden variable framework should consult this ob- tum states can be understood as states of incomplete scure paper: Ref.
    [Show full text]