Quantum Theory: Informational Foundations and Foils

Chiribella, Giulio; Giulio Chiribella, Robert W. Spekkens Editors.-<br/>

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Quantum Theory: Informational Foundations and Foils

Chiribella, Giulio

ISBN:9789401773027
Main Entry: Chiribella, Giulio
Title:Quantum Theory: Informational Foundations and Foils/ Giulio Chiribella, Robert W. Spekkens Editors.-
Publisher:Dordrecht: Springer, 2016.

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Contents
Introduction
- 1 Characteristics of the New Wave of Quantum Foundations
- 2 Frameworks for Operational Theories
- 3 Book Synopsis
- 4 Concluding Remarks
- References
Part I Foil Theories
Optimal Information Transfer and Real-Vector-Space Quantum Theory
- 1 Introduction
- 2 Real-Vector-Space Quantum Theory
- 3 Optimal Transfer of Information: The Two-Dimensional Case
- 4 Optimal Transfer of Information: The d-Dimensional Case
- 5 Optimal Information Transfer in Standard Quantum Mechanics?
- 6 Conclusions
- References
Almost Quantum Theory
- 1 Introductory Remarks
- 2 Modal Quantum Theory
- 3 States and Measurements
- 4 Open System Evolution
- 5 Generalized Modal Theories
- 6 Concluding Remarks
  - 6.1 What MQT Has, and What It Does not Have
  - 6.2 Open Problems
- References
Quasi-Quantization: Classical Statistical Theories with an Epistemic Restriction
- 1 Introduction
- 2 Quadrature Epistricted Theories
- 3 Quadrature Quantum Subtheories
  - 3.1 Quadrature Observables
  - 3.2 Characterization of Quadrature Quantum Subtheories
- 4 Comparing Quantum Subtheories to Epistricted Theories
  - 4.1 Equivalence for Continuous and Odd-Prime Discrete Cases
  - 4.2 Inequivalence for Bits/Qubits
- References
Part II Axiomatizations
Information-Theoretic Postulates for Quantum Theory
- 1 Introduction
- 2 What Do We Mean by ``Quantum Theory''?
- 3 Generalized Probabilistic Theories
- 4 The Postulates
- 5 How Quantum Theory Follows from the Postulates
- 6 Conclusions and Outlook
- References
Quantum from Principles
- 1 Introduction
- 2 Operational-Probabilistic Theories
  - 2.1 Operational Structure
  - 2.2 Probabilistic Structure
- 3 Background of the Quantum Reconstruction
  - 3.1 Standing Assumptions
  - 3.2 Basic Operational Tasks
- 4 The Principles
- 5 The Reconstruction of Quantum Theory
- 6 Conclusions
- References
Reconstructing Quantum Theory
- 1 Motivation
- 2 A Personal History of Reconstruction
- 3 The Circuit Framework
- 4 The Postulates
- 5 Outline of Reconstruction
- 6 Conclusions
- References
The Classical Limit of a Physical Theory and the Dimensionality of Space
- 1 Introduction
- 2 The Classical Limit of Quantum Theory and Three-Dimensionality of Space
- 3 Generalized Spins and Higher-Dimensional Space
  - 3.1 Single System
  - 3.2 Generalized Spin-Coherent States
- 4 Dynamics and Macroscopic Limit
- 5 Covariant Interaction
- 6 Main Proofs
- 7 Going Beyond Three Dimensions
- 8 Conclusions
- References
Some Negative Remarks on Operational Approaches to Quantum Theory
- References
Part III Categories and Convex Sets
Generalised Compositional Theories and Diagrammatic Reasoning
- 1 Introduction to Quantum Picturalism
- 2 Pure State Quantum Mechanics
- 3 Complementarity and Strong Complementarity
- 4 Mixed States, Measurements, and ``Abstract Probabilities''
  - 4.1 Measurements and Born Vectors
- 5 Example: Non-locality of QM
- 6 Summary and Further Reading
- References
Post-Classical Probability Theory
- 1 Introduction
- 2 Elementary Probability Theory, Classical and Otherwise
- 3 Composition and Entanglement
- 4 Post-Classical Information Processing
- 5 Characterizing Quantum Theory
- 6 Conclusion
- References
Part IV Quantum Versus Super-QuantumCorrelations
Information Causality
- 1 Certain Things Should Not Happen
- 2 The Context
- 3 Information Causality: The Task
- 4 Mathematics
- 5 (Un?)expected Complexity
- 6 Conclusion
- References
Macroscopic Locality
- 1 Introduction
- 2 Macroscopic Locality
- 3 Quantum Mechanics Satisfies Macroscopic Locality
- 4 Predictions of ML
  - 4.1 The Bipartite Case
  - 4.2 The Tripartite Case
- 5 Conclusion
- References
Guess Your Neighbour's Input: No Quantum Advantage but an Advantage for Quantum Theory
- 1 Introduction
- 2 Guess Your Neighbour's Input
- 3 Application 1: Gleason's Theorem for Multipartite Systems
  - 3.1 Gleason Correlations
- 4 Application II: Quantum Correlations and Information Principles
  - 4.1 Time-Ordered-Bilocal Correlations and GYNI
- 5 Generalization of GYNI: Bell Inequalities Without Quantum Violation and Unextendible Product Bases
- 6 Conclusions
- References
The Completeness of Quantum Theory for Predicting Measurement Outcomes
- 1 Introduction
- 2 Preliminaries
- 3 Quantum and Alternative Theories
- 4 Freedom of Choice
  - 4.1 Causal Order
  - 4.2 Free Random Variables
- 5 Constraints on Theories Compatible with Quantum Theory
- 6 The Non-extendibility Theorem
- 7 Proof of Theorem 3
- 8 Alternative Theories Are Equivalent to Quantum Theory
  - 8.1 Related Work
- 9 Discussion
- References

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