دانلود کتاب Semidefinite Programming in Quantum Information Science

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Title
Copyright
Contents
Preface
Author biographies
About this book
Part I The fundamentals
1 Linear programming
1.1 The basics
1.1.1 Feasibility
1.2 Geometric interpretation
1.2.1 Equality constraints
1.2.2 Inequality constraints
1.2.3 The feasible set
1.2.4 The objective function
1.3 Duality
1.4 Slack variables
1.5 Weak and strong duality
1.6 Concluding remarks
1.7 Advanced topics
1.7.1 Complementary slackness
1.7.2 Dual form of ℓ1 and ℓ∞ norms
1.8 Further reading
2 Semidefinite programming
2.1 Primal semidefinite programs
2.2 Duality
2.3 Weak and strong duality
2.4 Complementary slackness
2.5 Linear programs as special instances of semidefinite programs
2.6 Concluding remarks
2.7 Further reading
Part II Semidefinite programming in quantum information science
3 Quantum states
3.1 Quantum state estimation
3.1.1 Trace distance estimation
3.1.2 Fidelity estimation
3.1.3 Finite statistics
3.1.4 Relaxing the feasibility problem
3.1.5 Certificate of infeasibility
3.1.6 Geometrical interpretation
3.1.7 Property estimation
3.2 The quantum marginal problem
3.3 Concluding remarks
3.4 Further reading
3.5 Advanced topics
3.5.1 The fidelity SDP
4 Quantum measurements
4.1 Quantum measurement estimation
4.2 Quantum state discrimination I
4.2.1 Minimum-error quantum state discrimination
4.2.2 Binary state discrimination
4.2.3 Optimality conditions
4.2.4 Unambiguous quantum state discrimination
4.3 Quantum state discrimination II
4.3.1 Transforming the non-linear problem into a linear one
4.3.2 Generalised robustness of measurement informativeness
4.3.3 Structure of the optimal ensemble and noise measurement
4.4 Concluding remarks
4.5 Further reading
4.6 Advanced topics
4.6.1 Unambiguous quantum state discrimination revisited
5 Quantum entanglement
5.1 Entanglement of pure and mixed states
5.2 The positive-partial-transpose criterion
5.3 Entanglement negativity
5.4 Random robustness of entanglement and SDP relaxations
5.5 k-symmetric extensions
5.6 Concluding remarks
5.7 Further reading
5.8 Advanced topics
5.8.1 Entanglement witnesses from k-symmetric extensions
6 Measurement incompatibility
6.1 Joint measurability as an SDP
6.2 Two dichotomic measurements
6.3 Concluding remarks
6.4 Further reading
6.5 Advanced topics
6.5.1 Measurement incompatibility and quantum nonlocality
7 Quantum channels
7.1 The Choi–Jamiołkowski isomorphism
7.2 Channel estimation
7.3 The diamond norm and channel discrimination
7.4 The conditional min-entropy and the singlet fidelity
7.5 Concluding remarks
7.6 Further reading
7.7 Advanced topics