Simnacher, Timo Yannick: The interplay between quantum entanglement, coherence, and convex optimization. 2021
Inhalt
- Abstract
- Zusammenfassung
- Table of contents
- 1 Introduction
- 2 Mathematical fundamentals
- 2.1 Introduction
- 2.2 Quantum mechanics
- 2.3 Quantum channels
- 2.4 Coherence
- 2.5 Entanglement
- 2.6 Numerical range
- 2.7 The marginal problem and quantum codes
- 2.8 Semidefinite programming
- 2.9 Classical entropy and majorization
- 3 Quantum-inspired hierarchy for rank-constrained optimization
- 3.1 Introduction
- 3.2 Rank-constrained SDP and quantum entanglement
- 3.3 Examples
- 3.4 Arbitrary-precision certified semidefinite programming
- 3.5 More general results on rank-constrained optimization
- 3.6 Conclusion
- 4 A complete hierarchy for the pure-state marginal problem in quantum mechanics
- 4.1 Introduction
- 4.2 Connecting the marginal problem with the separability problem
- 4.3 Absolutely maximally entangled states
- 4.4 Multi-party extension: primal problem
- 4.5 Multi-party extension: dual problem and entanglement witness
- 4.6 Multi-party extension: PPT criterion with respect to any bipartition
- 4.7 Quantum codes
- 4.8 Conclusion
- 5 Entanglement detection with scrambled data
- 5.1 Introduction
- 5.2 Setup and Definitions
- 5.3 Entropic uncertainty relations
- 5.4 Scrambling-invariant families of entanglement witnesses
- 5.5 Nonconvex structure of the nondetectable state space
- 5.6 Conclusion
- 6 Confident entanglement detection via numerical range
- 6.1 Introduction
- 6.2 Experimental confidence region
- 6.3 Minimal volume ratio
- 6.4 Geometric considerations
- 6.5 Two qubits
- 6.6 Commutativity and entanglement detection
- 6.7 Conclusion
- 7 Certifying quantum memories with coherence
- 7.1 Introduction
- 7.2 Memory quality measures
- 7.3 Definition of the measures
- 7.4 Properties of the measures
- 7.5 The single-qubit case
- 7.6 Examples of single-qubit channels
- 7.7 Experimental estimation of the quality of a quantum memory
- 7.8 Conclusion
- Concluding remarks
- Acknowledgments
- List of publications
- List of Figures and Tables
- A Projectors onto invariant subspaces of partially transposed fourpartite permutation matrices
- Bibliography