Quantum Information Theory and the Foundations of Quantum Mechanics. [thesis]

C. Timpson

Table of contents :
Introduction……Page 7
I What is Information?……Page 12
How to talk about information: Some simple ways……Page 14
Interpretation of the Shannon Information……Page 21
More on communication channels……Page 27
Interlude: Abstract/concrete; technical, everyday……Page 31
Aspects of Quantum Information……Page 33
Information is Physical: The Dilemma……Page 40
Alternative approaches: Dretske……Page 45
Summary……Page 50
Introduction……Page 52
Are pre-existing bit-values required?……Page 54
The grouping axiom……Page 58
Brukner and Zeilinger’s `Total information content’……Page 65
Some Different Notions of Information Content……Page 67
The Relation between Total Information Content and I()……Page 70
Conclusion……Page 74
Introduction……Page 75
The quantum teleportation protocol……Page 76
Some information-theoretic aspects of teleportation……Page 78
The puzzles of teleportation……Page 80
Resolving (dissolving) the problem……Page 82
The simulation fallacy……Page 84
The teleportation process under different interpretations……Page 87
Collapse interpretations: Dirac/von Neumann, GRW……Page 88
No collapse and no extra values: Everett……Page 89
No collapse, but extra values: Bohm……Page 91
Ensemble and statistical viewpoints……Page 97
Concluding remarks……Page 98
Introduction……Page 103
The Deutsch-Hayden Picture……Page 105
Locality claim (2): Contiguity……Page 110
Assessing the Claims to Locality……Page 113
The Conservative Interpretation……Page 114
The Ontological Interpretation……Page 118
Information and Information Flow……Page 122
Whereabouts of information……Page 123
Explaining information flow in teleportation: Locally accessible and inaccessible information……Page 125
Assessing the claims for information flow……Page 128
Conclusion……Page 134
Entanglement in Deutsch-Hayden……Page 137
Background……Page 139
Entanglement witnesses and the Horodecki’s PPT condition……Page 140
The majorization condition……Page 145
The tetrahedron of Bell-diagonal states……Page 147
Characterizations in the Deutsch-Hayden representation……Page 150
Some sufficient conditions for entanglement……Page 152
The PPT and reduction criteria……Page 154
Summary……Page 160
Introduction……Page 162
Quantum computation and containing information……Page 164
The Turing Principle versus the Church-Turing Hypothesis……Page 165
Non-Turing computability? The example of Malament-Hogarth spacetimes……Page 174
Lessons……Page 177
The Church-Turing Hypothesis as a constraint on physics?……Page 178
Morals……Page 182
II Information and the Foundations of Quantum Mechanics……Page 185
Information Talk in Quantum Mechanics……Page 187
Some Information-Theoretic Approaches……Page 194
Zeilinger’s Foundational Principle……Page 195
Word and world: Semantic ascent……Page 201
Shannon information and the Foundational Principle……Page 204
The Clifton-Bub-Halvorson characterization theorem……Page 207
The setting……Page 208
Some queries regarding the C*-algebraic starting point……Page 216
Questions of Interpretation……Page 224