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Bell Nonlocality [Kietas viršelis]

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(Principle Investigator and Professor, National University of Singapore)
  • Formatas: Hardback, 240 pages, aukštis x plotis x storis: 248x176x17 mm, weight: 633 g, 18 grayscale line drawings
  • Serija: Oxford Graduate Texts
  • Išleidimo metai: 13-Aug-2019
  • Leidėjas: Oxford University Press
  • ISBN-10: 019878841X
  • ISBN-13: 9780198788416
Kitos knygos pagal šią temą:
Bell NonlocalityDidesnis paveikslėlis
  • Formatas: Hardback, 240 pages, aukštis x plotis x storis: 248x176x17 mm, weight: 633 g, 18 grayscale line drawings
  • Serija: Oxford Graduate Texts
  • Išleidimo metai: 13-Aug-2019
  • Leidėjas: Oxford University Press
  • ISBN-10: 019878841X
  • ISBN-13: 9780198788416
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780198788416.html
Raktažodžiai:
This is an open access title. It is made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International licence. It is available to read and download as a PDF version on the Oxford Academic platform.

The development of quantum technologies has seen a tremendous upsurge in recent years, and the theory of Bell nonlocality has been key in making these technologies possible. Bell nonlocality is one of the most striking discoveries triggered by quantum theory. It states that in some situations, measurements of physical systems do not reveal pre-existing properties; rather, the property is created by the measurement itself. In 1964, John Bell demonstrated that the predictions of quantum theory are incompatible with the assumption that outcomes are predetermined. This phenomenon has been observed beyond any doubt in the last decades. It is an observation that is here to stay, even if quantum theory were to be replaced in the future. Besides having fundamental implications, nonlocality is so specific that it can be used to develop and certify reliable quantum devices.

This book is a logical, rather than historical, presentation of nonlocality and its applications. Part 1 opens with a survey of the meaning of Bell nonlocality and its interpretations, then delves into the mathematical formalisation of this phenomenon, and finally into its manifestations in quantum theory. Part 2 is devoted to the possibility of using the evidence of nonlocality for certification of devices for quantum technologies. Part 3 explores some of the extensions and consequences of nonlocality for the foundations of physics.
Part I Classic Bell Nonlocality
1 First Encounter with Bell Nonlocality
3(22)
1.1 Three Roles for Bell Nonlocality
3(1)
1.2 Introducing Bell Nonlocality
4(4)
1.3 My First Bell Test: Clauser-Horne-Shimony-Holt (CHSH)
8(3)
1.4 Four more Classic Bell Tests
11(3)
1.5 A Closer Scrutiny: Addressing Loopholes
14(5)
1.6 Experimental Metaphysics?
19(6)
2 Formalizing Bell Nonlocality
25(18)
2.1 Bell Scenarios, Processes, and Behaviors
25(2)
2.2 No-Signaling Processes and Behaviors
27(2)
2.3 Local Behaviors
29(4)
2.4 The Local Polytope and Bell Inequalities
33(4)
2.5 The CHSH Scenario
37(3)
2.6 Proper Statistics: Beyond i.i.d. and Finite Samples
40(3)
3 Bell Nonlocality in Quantum Theory
43(12)
3.1 Quantum Behaviors
43(2)
3.2 CHSH in Quantum Theory
45(6)
3.3 Mixed Entangled States as Nonlocal Resources
51(4)
4 Review of Bipartite Bell Scenarios
55(10)
4.1 Unanticipated Complexity
55(1)
4.2 Several Inputs, Two Outputs
56(3)
4.3 Two Inputs, Several Outputs
59(2)
4.4 Hardy's Test and the Magic Square
61(4)
5 Multipartite Bell Nonlocality
65(12)
5.1 Definition and Systematic Results
65(3)
5.2 Examples of Multipartite Bell Inequalities
68(2)
5.3 Various Scenarios of Multipartite Nonlocality
70(7)
Part II Nonlocality as a Tool for Certification
6 The Set of Quantum Behaviors
77(9)
6.1 Device-Independent Certification: A First Introduction
77(1)
6.2 Definition and Geometry of the Quantum Set
78(3)
6.3 Semidefinite Relaxations of the Quantum Set
81(5)
7 Device-Independent Self-Testing
86(12)
7.1 Self-Testing of the Maximal Violation of CHSH
86(3)
7.2 The Mayers-Yao Self-Testing Behavior
89(4)
7.3 Formal Definition and its Consequences
93(1)
7.4 Approximate Self-Testing: Robustness Bounds
94(4)
8 Certifying Randomness
98(19)
8.1 Introduction to Randomness
98(5)
8.2 Quantification of Randomness
103(4)
8.3 Device-Independent Certification of Randomness
107(4)
8.4 Device-Independent Quantum Key Distribution
111(6)
Part III Foundational Insights from Nonlocality
9 Nonlocality in the No-Signaling Framework
117(12)
9.1 The No-Signaling Polytope
117(2)
9.2 The PR-Box
119(4)
9.3 Device-Independent Certification Reloaded
123(1)
9.4 Refinements on Quantum Indeterminacy
124(5)
10 The Quest for Device-Independent Quantum Principles
129(13)
10.1 Context: The Definition of Quantum Theory
129(1)
10.2 Information Causality
130(6)
10.3 Macroscopic Locality
136(3)
10.4 Local Orthogonality, a.k.a Consistent Exclusivity
139(1)
10.5 The Current Barrier: The "Almost-Quantum" Set
140(2)
11 Signaling and Measurement Dependence
142(15)
11.1 Motivation: Towards Ultimate Relaxations
142(1)
11.2 Signaling Models: The Information in the Communication
143(2)
11.3 Signaling Models: The Speed of the Influence
145(4)
11.4 Relaxing Measurement Independence
149(3)
11.5 Randomness Amplification
152(5)
12 Epilogue
157(2)
Appendix A History Museum
159(3)
A.1 Heisenberg's Uncertainty Relations and the Question of Indeterminism
159(1)
A.2 The EPR Argument
160(1)
A.3 Von Neumann's Observation on Pre-Established Values
161(1)
A.4 Bell's 1964 Inequality
161(1)
Appendix B Experimental Platforms: A Reading Guide
162(5)
B.1 Photons
162(2)
B.2 Atomic Degrees of Freedom
164(1)
B.3 How to Address the Detection Loophole
164(3)
Appendix C Notions of Quantum Theory Used in this Book
167(7)
C.1 States and Measurements
167(2)
C.2 Elementary Entanglement Theory
169(2)
C.3 Generalized Measurements or POVMs
171(3)
Appendix D LV Models for Single Systems
174(5)
D.1 Overview: Looking into Measurements
174(1)
D.2 Bell's Local Hidden Variable Model for One Qubit
175(1)
D.3 Contextuality
175(4)
Appendix E Basic Notions of Convex Optimization
179(4)
E.1 Generalities
179(2)
E.2 Two Explicit Examples
181(2)
Appendix F Device-Independent Certification: History and Review
183(11)
F.1 Bell Nonlocality and Quantum Information Science
183(3)
F.2 Overview of Tasks
186(2)
F.3 Device-Independent, Really?
188(1)
F.4 Certification with Partially Characterized Devices
189(5)
Appendix G Repository of Technicalities
194(13)
G.1 Analytical Solution of the Facets of the CHSH Correlation Polytope
194(1)
G.2 Hardy's Test from the Schmidt Decomposition of the State
195(2)
G.3 Pitfalls in Handling Signaling Behaviors
197(1)
G.4 Jordan's Lemma
198(1)
G.5 A Case Study of Randomness with Characterised Devices
199(2)
G.6 Simulations of the Singlet Behavior
201(2)
G.7 Properties of the Variational Distance
203(1)
G.8 Information Causality from Desiderata on Information Entropies
204(3)
References 207(16)
Index 223
Valerio Scarani was born in Milan in 1972. He graduated from Ecole Polytechnique Federale de Lausanne in 1996 and received his doctorate in physics from the same institution in 2000. He then moved to the University of Geneva, where he started working on quantum information science, notably quantum cryptography and Bell nonlocality. In 2007 he joined the National University of Singapore, as a member of the Physics Department and Principal Investigator at the Centre for Quantum Technologies.