Philosophy of Quantum Information and Entanglement

✍ Scribed by Bokulich A., Jaeger G. (eds.)

• Publisher: CUP
• Year: 2010
• Tongue: English
• Leaves: 309
• Category: Library

✦ Synopsis

Recent work in quantum information science has produced a revolution in our understanding of quantum entanglement. Scientists now view entanglement as a physical resource with many important applications. These range from quantum computers, which would be able to compute exponentially faster than classical computers, to quantum cryptographic techniques, which could provide unbreakable codes for the transfer of secret information over public channels. These important advances in the study of quantum entanglement and information touch on deep foundational issues in both physics and philosophy. This interdisciplinary volume brings together fourteen of the world's leading physicists and philosophers of physics to address the most important developments and debates in this exciting area of research. It offers a broad spectrum of approaches to resolving deep foundational challenges - philosophical, mathematical, and physical - raised by quantum information, quantum processing, and entanglement. This book is ideal for historians, philosophers of science and physicists.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contributors......Page 11
Preface......Page 13
Introduction......Page 15
References......Page 30
Part I Quantum entanglement and non-locality......Page 33
1.1 Introduction......Page 35
1.2 Non-local correlations beyond quantum mechanics......Page 37
1.3 Communication complexity......Page 39
1.4 Non-local computation......Page 42
1.5 Conclusions......Page 45
References......Page 46
2.1 Introduction......Page 48
2.2 Entanglement and subsystems: the standard view......Page 50
2.3 Entanglement beyond subsystems: the concept of generalized entanglement......Page 54
2.3.1 Generalized-entanglement settings......Page 56
2.3.2 Generalized-entanglement measures......Page 57
2.4.1 Entanglement with respect to local observables......Page 58
2.4.1.2 A three-qubit case study......Page 59
2.4.1.3 The convex cones setting; GE in Popescu–Rohrlich boxes......Page 61
2.4.2 Entanglement without locality . . .......Page 65
2.4.3 Separability without entanglement . . .......Page 66
2.4.4 Fermionic entanglement......Page 67
2.5.1 Complexity implications......Page 69
2.5.2 Classicality implications......Page 70
2.5.3 Conceptual implications and unresolved problems......Page 71
References......Page 72
3.1 Introduction......Page 76
3.2 Dealing with indefinite causal structure......Page 78
3.2.1 Issue 1: the need for a two-step approach......Page 79
3.2.2 Issue 2: the need for F-locality......Page 80
3.3 How standard formulations of physical theories are not F-local......Page 81
3.4 An outline of the causaloid framework......Page 82
3.4.2 p-Type vectors and r-type vectors......Page 83
3.4.3 The causaloid product......Page 85
3.4.4 The two-step approach in the causaloid framework......Page 86
3.5 Formulating quantum theory in the causaloid framework......Page 87
3.6 The road to quantum gravity......Page 90
3.7 Conclusions......Page 92
References......Page 93
Part II Quantum probability......Page 95
4.1.1 Quantum information and quantum foundations......Page 97
4.1.2 Bell’s inequality......Page 99
4.2.1 Bell’s inequality......Page 100
4.2.2 Wigner’s inequality......Page 101
4.2.3 The Clauser–Horne–Shimony–Holt inequality......Page 102
4.3 Formalization of rules for correspondence between classical and quantum statistical models......Page 103
4.4 Von Neumann postulates on classical–quantum correspondence and the no-go theorem......Page 104
4.5 Bell-type no-go theorems......Page 105
4.6 The range-of-values postulate......Page 109
4.7.1 Non-injectivity of classical rarrow quantum correspondence......Page 110
4.7.2 Contextual opposition against Bell’s approach to no-go theorems......Page 111
4.8 Bell-contexuality and action at a distance......Page 113
Acknowledgments......Page 114
References......Page 115
5.1 Introduction......Page 117
5.2.1 Tests and states......Page 122
5.2.2 Cascading, conditioning, and transformations......Page 123
5.2.4 Effects......Page 125
5.2.5 Linear structures for transformations and effects......Page 127
5.2.6 Observables and informational completeness......Page 129
5.2.8 The Metric......Page 130
5.2.9 Isometric transformations......Page 131
5.2.10 The C-algebra of transformations......Page 132
5.3.1 Dynamical independence and marginal states......Page 134
5.3.2 Faithful states......Page 136
5.3.3 The Scalar product over effects induced by a symmetric faithful state......Page 142
5.4.1 FAITHE: a postulate on a faithful effect......Page 143
5.4.2 PURIFY: a postulate on purifiability of all states......Page 147
5.5 What is special about quantum mechanics as a probabilistic theory?......Page 148
5.5.1 Building up an associative algebra structure for complex effects......Page 149
5.5.2 Building up a C-algebra structure over complex effects......Page 150
5.5.3 Recovering the action of transformations over effects......Page 151
5.6 Conclusions......Page 153
Acknowledgments......Page 155
References......Page 156
6.1 Introduction......Page 159
6.2 Parameter spaces and quantum models......Page 161
6.2.1 Measure spaces......Page 162
6.2.3 Quantum models......Page 163
6.3 Many quantum models of any PPM......Page 165
6.3.1 Application of non-uniqueness of models to the Holevo bound......Page 167
6.3.2 An example from quantum cryptography of an enveloping PPM......Page 168
6.4.1 Formulation......Page 171
6.4.2 EPR......Page 172
6.4.3 Generalized Bell inequalities and their violation......Page 173
6.4.5 Case study of a toroidal parameter space......Page 174
6.4.6 Allowing for elliptical polarization: SO(3)......Page 177
6.4.8 Allowing for light frequency, etc.......Page 179
Acknowledgments......Page 180
References......Page 181
7.1 Introduction......Page 183
7.3 Quantum measurement......Page 184
7.4 Quantum measurement as Bayesian updating......Page 185
7.5.1 Information gain......Page 192
7.5.2 Information gain in quantum measurements......Page 194
7.5.3 Generalized Bayesian measurements and information gain......Page 195
7.5.4 Inefficient measurements and information loss......Page 197
7.6 Conclusion......Page 198
References......Page 199
Part III Quantum information......Page 201
8.1 Introduction......Page 203
8.2 The CBH theorem......Page 204
8.3 Quantum information......Page 207
8.4 Re-conceiving quantum mechanics......Page 208
References......Page 211
9.1 Introduction......Page 213
9.2 Algebraic frameworks......Page 215
9.3 The operational approach......Page 218
9.4 The convex-set approach......Page 220
9.5 The Spekkens toy theory......Page 226
9.6.1 C-and JB algebras......Page 236
Acknowledgments......Page 237
References......Page 238
10.1 Two thoughts......Page 240
10.2 The quantum state as information......Page 243
10.3 Against “information”......Page 246
10.3.1 The problem of factivity......Page 247
10.4 If not instrumentalism, axiomatics instead?......Page 249
10.5 Why the quantum?......Page 253
10.6 Conclusion......Page 256
References......Page 257
Part IV Quantum communication and computing......Page 261
11.1 Introduction......Page 263
11.2 Deutsch’s XOR algorithm......Page 264
11.3 Period-finding algorithms......Page 269
11.4 Conclusion......Page 275
Acknowledgments......Page 277
References......Page 278
12.1 Introduction......Page 279
12.2 Quantum memory......Page 280
12.3 A potential model of quantum memory......Page 283
12.4 Write, read, and reset......Page 284
12.5 Decoherence due to the finite length of the pulse......Page 288
12.6 Quantum cryptography......Page 291
12.7 The Fermi pseudo-potential in one dimension......Page 296
12.8 Conclusion and discussions......Page 301
References......Page 303
Index......Page 306