Gachechiladze, Mariami: Quantum hypergraph states and the theory of multiparticle entanglement. 2019
Inhalt
- Abstract
- Zusammenfassung
- Contents
- 1 Introduction
- 2 Preliminaries
- 2.1 Quantum states and their entanglement
- 2.1.1 Bipartite entanglement
- 2.1.2 Multipartite entanglement
- 2.1.3 Local manipulation of entanglement
- 2.1.4 Entanglement measures
- 2.1.5 Entanglement Witnesses
- 2.2 Nonlocality
- 2.3 Quantum computation
- 2.4 Multipartite pure states and their applications
- 2.4.1 Graph states
- 2.4.1.1 Constructing graph states
- 2.4.1.2 Stabilizer Formalism
- 2.4.1.3 Local unitary equivalent graph states
- 2.4.1.4 Pauli measurement rules for graph states
- 2.4.1.5 Bell inequalities for graph states
- 2.4.1.6 Measurement-based quantum computation
- 2.4.1.7 Graph states in quantum error-correction
- 2.4.2 Hypergraph states
- 2.4.2.1 Constructing hypergraph states
- 2.4.2.2 Nonlocal stabilizer formalism
- 2.4.2.3 Local Pauli equivalences of hypergraph states
- 2.4.3 Linear matrix pencil states
- 3 Extreme violation of local realism in quantum hypergraph states
- 3.1 Introduction
- 3.2 Local correlations from nonlocal stabilizer
- 3.3 Hardy-type arguments and nonlocality proofs
- 3.4 Genuine multiparticle nonlocality
- 3.5 Extreme violation in complete three-uniform states
- 3.6 Extreme violation in complete four-uniform states
- 3.7 Robustness of violation
- 3.8 Applications and Outlook
- 4 Graphical rules for transformations on hypergraph states
- 4.1 Introduction
- 4.2 Local complementation in hypergraph states
- 4.3 Graphical rules for permutation unitaries on hypergraph states
- 4.4 Pauli measurement rules on hypergraph states
- 4.5 Summary and outlook
- 5 Quantifying and detecting entanglement in hypergraph states
- 5.1 Introduction
- 5.2 Entanglement detection for hypergraph states
- 5.3 Geometric Measure of hypergraph states
- 5.4 Summary and outlook
- 6 Changing circuit-depth complexity of MBQC with hypergraph states
- 6.1 Introduction
- 6.2 Summary of computation scheme
- 6.3 Universal three-uniform hypergraph state and deterministic MBQC
- 6.4 Applications of computation scheme
- 6.5 Summary and outlook
- 7 Quantum error-correction and hypergraph states
- 7.1 Introduction
- 7.2 Conditions for distance two hypergraph-based QECC
- 7.3 Hypergraph based codes of distance two
- 7.4 Summary and outlook
- 8 Coarse graining of entanglement classes in nonhomogeneous systems
- 8.1 Introduction
- 8.2 SLOCC classes containing generic states
- 8.3 Common resource states for generic states
- 8.4 Common resource states for all states
- 8.5 Summary and outlook
- 9 Entanglement detection with two observables
- 9.1 Introduction
- 9.2 Formulation with Legendre transformation
- 9.3 Criterion for various scenarios
- 9.4 Summary and outlook
- 10 Pure entangled states are Bell nonlocal
- 10.1 Introduction
- 10.2 Discussion of the original argument
- 10.3 Completing the argument
- 10.4 Projecting on genuine multipartite entanglement
- 10.5 Summary and outlook
- Conclusions and outlook
- Acknowledgements
- List of publications
- A An Appendix to Chapter 3
- A.1 Complete three-uniform hypergraph correlations
- A.2 Complete four-uniform hypergraph correlations
- A.3 Bell and separability inequalities for noisy four-uniform states
- A.4 Separability inequality for noisy three-uniform states
- B An Appendix to Chapter 5
- C An Appendix to Chapter 7
- D An Appendix to Chapter 8
- Bibliography