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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. -
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. -
Testing the Quantum-Classical Boundary and Dimensionality of Quantum Systems
Testing the Quantum-Classical Boundary and Dimensionality of Quantum Systems Poh Hou Shun Centre for Quantum Technologies National University of Singapore This dissertation is submitted for the degree of Doctor of Philosophy September 2015 Acknowledgements No journey of scientific discovery is ever truly taken alone. Every step along the way, we encounter people who are a great source of encouragement, guidance, inspiration, joy, and support to us. The journey I have embarked upon during the course of this project is no exception. I would like to extend my gratitude to my project partner on many occasion during the past 5 years, Ng Tien Tjeun. His humorous take on various matters ensures that there is never a dull moment in any late night lab work. A resounding shout-out to the ‘elite’ mem- bers of 0205 (our office), Tan Peng Kian, Shi Yicheng, and Victor Javier Huarcaya Azanon for their numerous discourses into everything under the sun, some which are possibly work related. Thank for tolerating my borderline hoarding behavior and the frequently malfunc- tioning door? I would like to thank Alessandro Ceré for his invaluable inputs on the many pesky problems that I had with data processing. Thanks for introducing me to world of Python programming. Now there is something better than Matlab? A big thanks also goes out to all of my other fellow researchers and colleagues both in the Quantum Optics group and in CQT. They are a source of great inspiration, support, and joy during my time in the group. Special thanks to my supervisor, Christian Kurtsiefer for his constant guidance on and off the project over the years. -
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 -
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. -
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. -
Report to Industry Canada
Report to Industry Canada 2013/14 Annual Report and Final Report for 2008-2014 Granting Period Institute for Quantum Computing University of Waterloo June 2014 1 CONTENTS From the Executive Director 3 Executive Summary 5 The Institute for Quantum Computing 8 Strategic Objectives 9 2008-2014 Overview 10 2013/14 Annual Report Highlights 23 Conducting Research in Quantum Information 23 Recruiting New Researchers 32 Collaborating with Other Researchers 35 Building, Facilities & Laboratory Support 43 Become a Magnet for Highly Qualified Personnel in the Field of Quantum Information 48 Establishing IQC as the Authoritative Source of Insight, Analysis and Commentary on Quantum Information 58 Communications and Outreach 62 Administrative and Technical Support 69 Risk Assessment & Mitigation Strategies 70 Appendix 73 2 From the Executive Director The next great technological revolution – the quantum age “There is a second quantum revolution coming – which will be responsible for most of the key physical technological advances for the 21st Century.” Gerard J. Milburn, Director, Centre for Engineered Quantum Systems, University of Queensland - 2002 There is no doubt now that the next great era in humanity’s history will be the quantum age. IQC was created in 2002 to seize the potential of quantum information science for Canada. IQC’s vision was bold, positioning Canada as a leader in research and providing the necessary infrastructure for Canada to emerge as a quantum industry powerhouse. Today, IQC stands among the top quantum information research institutes in the world. Leaders in all fields of quantum information science come to IQC to participate in our research, share their knowledge and encourage the next generation of scientists to continue on this incredible journey. -
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. -
Many-Body Entanglement in Classical & Quantum Simulators
Many-Body Entanglement in Classical & Quantum Simulators Johnnie Gray A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London. Department of Physics & Astronomy University College London January 15, 2019 2 3 I, Johnnie Gray, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the work. Abstract Entanglement is not only the key resource for many quantum technologies, but es- sential in understanding the structure of many-body quantum matter. At the interface of these two crucial areas are simulators, controlled systems capable of mimick- ing physical models that might escape analytical tractability. Traditionally, these simulations have been performed classically, where recent advancements such as tensor-networks have made explicit the limitation entanglement places on scalability. Increasingly however, analog quantum simulators are expected to yield deep insight into complex systems. This thesis advances the field in across various interconnected fronts. Firstly, we introduce schemes for verifying and distributing entanglement in a quantum dot simulator, tailored to specific experimental constraints. We then confirm that quantum dot simulators would be natural candidates for simulating many-body localization (MBL) - a recently emerged phenomenon that seems to evade traditional statistical mechanics. Following on from that, we investigate MBL from an entanglement perspective, shedding new light on the nature of the transi- tion to it from a ergodic regime. As part of that investigation we make use of the logarithmic negativity, an entanglement measure applicable to many-body mixed states. -
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. -
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. -
CURRICULUM VITA N. David Mermin Laboratory of Atomic and Solid State Physics Clark Hall, Cornell University, Ithaca, NY 14853-2501
CURRICULUM VITA N. David Mermin Laboratory of Atomic and Solid State Physics Clark Hall, Cornell University, Ithaca, NY 14853-2501 Born: 30 March 1935, New Haven, Connecticut, USA Education: 1956 A.B., Harvard (Mathematics, summa cum laude) 1957 A.M., Harvard (Physics) 1961 Ph.D., Harvard (Physics) Positions: 1961 - 1963 NSF Postdoctoral Fellow, University of Birmingham, England 1963 - 1964 Postdoctoral Associate, University of California, San Diego 1964 - 1967 Assistant Professor, Cornell University 1967 - 1972 Associate Professor, Cornell University 1972 - 1990 Professor, Cornell University 1984 - 1990 Director, Laboratory of Atomic and Solid State Physics 1990 - 2006 Horace White Professor of Physics, Cornell University 2006 - Horace White Professor of Physics Emeritus, Cornell University Visiting Positions and Lecturerships: 1970 - 1971 Visiting Professor, Instituto di Fisica \G. Marconi," Rome 1978 - 1979 Senior Visiting Fellow, University of Sussex 1980 Morris Loeb Lecturer, Harvard University 1981 Emil Warburg Professor, University of Bayreuth 1982 Phillips Lecturer, Haverford College 1982 Japan Association for the Advancement of Science Fellow, Nagoya 1984 Walker-Ames Professor, University of Washington 1987 Welch Lecturer, University of Toronto 1990 Sargent Lecturer, Queens University, Kingston Ontario 1991 Joseph Wunsch Lecturer, the Technion, Haifa 1993 Feenberg Lecturer, Washington University, St. Louis 1993 Guptill Lecturer, Dalhousie University, Halifax 1994 Chesley Lecturer, Carleton College 1995 Lorentz Professor, University