Ritz, Christina: Characterizing the structure of multiparticle entanglement in high-dimensional systemsCharakterisierung von Vielteilchenverschränkung in hochdimensionalen Systemen. 2018
Inhalt
- Abstract
- Zusammenfassung
- Contents
- List of Figures
- List of Tables
- 1 Introduction
- 2 Preliminaries
- 2.1 Mathematical framework
- 2.1.1 Hilbert space
- 2.1.2 Quantum states in Hilbert space
- Pure quantum states
- The coefficient matrix of pure quantum states
- Schmidt decomposition
- Mixed quantum states
- Reduced quantum states
- 2.1.3 Quantum operations
- 2.2 Entanglement
- 2.3 Entanglement classification and quantification
- 2.3.1 Classification
- 2.3.2 Quantification
- 2.3.3 Classification of bipartite entanglement
- 2.3.4 Classification of multipartite entanglement
- 2.4 Entanglement detection
- 2.4.1 PnCP-maps
- PPT-criterion
- Reduction criterion
- Majorization criterion
- Range criterion
- Matrix realignement criterion
- 2.4.2 Entanglement witnesses
- 2.5 Graph states, Hypergraph states and the Stabilizer formalism
- 3 Tensor witness
- 4 Hypergraph states in arbitrary, finite dimension
- 4.1 Phase space representation of quantum systems in finite Hilbert spaces
- 4.2 Qudit hypergraph states
- 4.2.1 Introduction
- 4.2.2 Background and basic definitions
- 4.2.3 Qudit hypergraph states
- 4.2.4 Properties of hypergraph states and the stabilizer formalism
- Local action of Pauli and Clifford groups
- Stabilizer formalism
- Local measurements in Z basis and ranks of the reduced states
- 4.2.5 SLOCC and LU classes of hypergraphs
- 4.2.6 Classification of qudit hypergraphs under SLOCC and LU
- 4.2.7 Classification of 3 x 3 x 3
- 4.2.8 Classification of 4 x 4 x 4
- 4.2.9 Conclusions
- 4.2.10 Appendix
- 4.3 Local complementation of qudit graph states in arbitrary dimension
- 4.4 Weighted hypergraphs
- 5 Characterizing genuine multilevel entanglement
- 5.1 Genuine multilevel entanglement
- 5.1.1 Introduction
- 5.1.2 The scenario
- 5.1.3 General theory for bipartite systems
- 5.1.4 Multiparticle systems
- 5.1.5 Conclusion
- 5.1.6 Appendix
- 5.2 Distinguishing MME from DEC
- 5.3 Lower dimensional representation of qudit graph states
- 5.4 Network configuration
- 6 Summary and Outlook
- Acknowledgements
- Appendix A - SLOCC classification of 233 systems
- Bibliography