Inhalt

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   Abstract
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   Zusammenfassung
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   Table of contents
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   1 Introduction
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  2 Mathematical toolbox
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   2.1 Introduction
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   2.2 Quantum mechanics and quantum states
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   2.3 Qubits and the Bloch basis
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   2.4 Marginal states
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   2.4.1 The marginal problem
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   2.4.2 Mathematical description
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   2.4.3 Previous results
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  2.5 Entanglement
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   2.5.1 Bipartite entanglement
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   2.5.2 Multipartite entanglement
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   2.5.3 Entanglement measures
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   2.5.4 Monogamy of entanglement
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   2.5.5 Witnesses
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   2.6 Quantum channels
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   2.6.1 The Kraus representation
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   2.6.2 The Choi-Jamiołkowski isomorphism
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   2.7 Entropy
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   2.7.1 The von Neumann entropy
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   2.7.2 The linear entropy
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  2.8 Coherence
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   2.8.1 Coherence measures
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   2.8.2 The l1-norm of coherence and robustness of coherence
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   2.9 Semidefinite programs
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  3 The marginal problem
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   3.1 Introduction
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   3.2 Motivation
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   3.3 Unique ground states and uniquely determined states
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  3.4 The four particle case
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   3.4.1 Generic states
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   3.4.2 The case of qubits
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   3.4.3 The case of higher-dimensional systems
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   3.5 States of n particles
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   3.6 States that are not UDP
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   3.7 Conclusions
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  4 Even and odd correlations
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   4.1 Introduction
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   4.2 The even-odd decomposition
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   4.3 Results for an odd number of qubits
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   4.4 Results for an even number of qubits
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  4.5 Applications
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   4.5.1 Ground states of Hamiltonians
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   4.5.2 Unitary time evolution
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   4.5.3 Entanglement detection
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  4.6 Generalizations
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   4.6.1 Mixed states
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   4.6.2 Higher dimensional systems
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   4.6.3 Generalized inversions
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   4.7 Conclusions
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  5 Sector lengths
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   5.1 Introduction
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   5.2 Basic definitions
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  5.3 Bounds on individual sector lengths
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   5.3.1 Bounds on A2
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   5.3.2 Bounds on A3 and higher sectors
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   5.3.3 Bounds on An
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   5.3.4 Application to entanglement detection
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   5.4 Bounds on linear combinations of sector lengths
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   5.4.1 Translation into entropy inequalities
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   5.4.2 Characterization of two-qubit states
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   5.4.3 Characterization of three-qubit states
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   5.4.4 Connection to strong subadditivity
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   5.4.5 A list of pure four-qubit states
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   5.5 Conclusions
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  6 Learning about entanglement from higher moments
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   6.1 Introduction
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   6.2 Moments of random correlation measurements
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   6.3 Spherical designs
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   6.4 The two-qubit case
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   6.4.1 The landscape of all two-qubit states
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   6.4.2 The subset of separable two-qubit states
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   6.5 Boundary states
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   6.6 Multipartite entanglement
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   6.7 Conclusions
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  7 Detecting entanglement using product observables
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   7.1 Introduction
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   7.2 The setting
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   7.3 Relation to entanglement witnesses
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   7.4 Systems of two qubits
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   7.5 Systems of higher dimensions
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   7.6 Connection to joint measurability
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   7.7 Conclusions
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  8 Certifying quantum memories
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   8.1 Introduction
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   8.2 Sources of errors in quantum memories
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   8.3 Existing quantum memory quality measures
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   8.4 Criteria for quality measures
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   8.5 A coherence based quality measure
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   8.6 Properties of the measures
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   8.7 Experimental estimation
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   8.8 Conclusions
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   Concluding remarks
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   Acknowledgments
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   List of publications
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  List of Figures and Tables
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   List of Figures
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   List of Tables
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   A A Sudoku-like game to prove sector length inequalities
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   B Sector length inequalities from projectors onto symmetric and antisymmetric subspaces
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   Bibliography