Miklin, Nikolai: Characterizing classical and quantum systems from marginal correlations. 2017
Inhalt
- Abstract
- Zusammenfassung
- Contents
- Symbols
- 1 Introduction
- 2 Preliminaries
- 2.1 Entanglement
- 2.1.1 Bipartite entanglement
- 2.1.2 Multipartite entanglement
- 2.1.3 SLOCC classification
- 2.1.4 Graph and hypergraph states
- 2.2 Nonlocality
- 2.3 Causal models
- 2.3.1 Directed and undirected graphs
- 2.3.2 Cause-effect relations
- 2.3.3 Bayesian networks
- 2.3.4 Markov random fields
- 2.3.5 Hidden variables
- 2.3.6 Causal models in Bell's test
- 2.3.7 Indefinite causal order
- 2.4 Marginal problem
- 2.5 Entropic inequalities
- 2.5.1 Entropy cone
- 2.5.2 Probability structures
- 2.5.3 The entropic characterization of Bayesian networks
- 2.5.4 The entropic characterization of counterfactuals
- 2.6 Semidefinite Programming
- 3 Multiparticle entanglement as an emergent phenomenon
- 3.1 Emergence of entanglement
- 3.2 Statement of the problem
- 3.3 Construction method
- 3.4 Results
- 3.4.1 Three qubits
- 3.4.2 Four and five qubits
- 3.4.3 Generalization to more particles
- 3.4.4 Uniqueness of the global state
- 3.5 Extensions of the problem
- 3.5.1 Separability of the higher-order marginals
- 3.5.2 Proving entanglement from a subset of marginals
- 3.5.3 Higher-dimensional systems
- 3.5.4 No localizable entanglement in the marginals
- 3.6 Conclusions
- 4 Qudit hypergraph states
- 4.1 Introduction
- 4.2 Definition of qudit hypergraph states
- 4.3 SLOCC and LU classes of hypergraphs
- 4.4 SLOCC classification of tripartite hypergraph states in dimensions 3 and 4.
- 4.5 Conclusions
- 5 Indistinguishability of causal relations from limited marginals
- 5.0.1 Properties of graphs and hypergraphs
- 5.1 Adhesivity and independence constraints associated with a marginal scenario
- 5.1.1 Adhesivity of probabilities
- 5.1.2 Marginal scenarios admitting a global extension
- 5.1.3 Maximal set of independence conditions associated with a marginal scenario
- 5.2 Optimal characterization of the marginal scenario for probabilities and entropies
- 5.2.1 Triangulation
- 5.2.2 Probabilities
- 5.2.3 Entropies
- 5.2.4 Outer approximations of the entropy cone
- 5.3 Indistinguishability of causal structures
- 5.4 Examples and computational results
- 5.5 Conclusions
- 6 The entropic approach to causal correlations
- 6.1 Introduction
- 6.2 Bipartite entropic causal inequalities
- 6.2.1 Characterization based on causal Bayesian networks
- 6.2.2 Characterization based on counterfactual variables
- 6.3 Multipartite entropic causal inequalities
- 6.4 Information bounds in causal games
- 6.5 Discussion
- Conclusions
- Appendix A - An Appendix to Chapter 6
- Bibliography
- List of publications
- Acknowledgments