Inhalt

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   Abstract
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   Zusammenfassung
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   Contents
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   Introduction
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  1. Preliminary notions
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   1.1 Hidden variable theories
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   1.2 Local hidden variables and Bell's theorem
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   Local hidden variables
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   CHSH inequality and Bell's theorem
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   Experimental tests
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   1.3 Noncontextual hidden variables and Kochen-Specker theorem
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   Noncontextual hidden variable theories
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   Kochen and Specker's original problem
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   Kochen-Specker theorem
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   State-independent contextuality
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  1.4 Macrorealist theories and Leggett-Garg inequalities
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   Macrorealist theories
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   Continuous variables
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   Quantum violations
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  1.5 Correlations polytopes
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   Definition
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   Examples
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  1.6 Tsirelson bound
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   Original argument
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   Semidefinite programming approach
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   1.7 Linear and semidefinite programming
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  2. Noncontextuality inequalities from variable elimination
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   2.1 Extension of measures and consistency conditions
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  2.2 Bell inequalities
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   CHSH polytope from Bell-Wigner polytope
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   Bipartite (2,n) scenario
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   Two parties, three settings
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   Bipartite (3,n) scenario
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   Multipartite (m,…,m,n) scenario
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   Computational results
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   2.3 Noncontextuality inequalities: The n-cycle scenario
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   2.4 Discussion
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  3. Optimal tests for state-independent contextuality
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   3.1 Optimization method
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  3.2 Applications
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   Yu and Oh
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   Extended Peres-Mermin set
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   Cabello, Estebaranz, and García-Alcaine's 18-vector proof
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   3.3 Experimental tests
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   3.4 Discussion
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   4. Quantum bounds for temporal correlations
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   4.1 Sequential projective measurements
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   4.2 The simplified method
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   4.3 The general method
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   4.4 Applications
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  4.5 Details of the calculations
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   Discussion of the simplest Leggett-Garg scenario
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   Detailed discussion of sequential bounds for the N-cycle inequalities
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   Completeness of the general method
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   Quantum bounds for compatible measurements in the N-cycle scenario
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   4.6 Discussion
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   5. Dimension witnesses
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  5.1 Noncontextuality and dimension witnesses
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   The KCBS inequality
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   The KCBS inequality with incompatible observables
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   The Peres-Mermin inequality
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   The PM inequality with incompatible observables
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   Imperfect measurements
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   Experimental results
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   Generalizations
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   5.2 Sequential measurements and Leggett-Garg inequality
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   The measurement scheme
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   A simple example
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   Asymptotic limit
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   Maximum violations
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   Temporal versus spatial correlations
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  5.3 Details of the calculations
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   Alternative proof of Observation 1
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   Detailed discussion of the N-cycle inequalities
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   Detailed proof of Observation 2
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   Proof of Observation 3
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   Imperfect measurements
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   Asymptotic value of the Leggett-Garg correlator for the precessing spin model
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   5.4 Discussion
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   Conclusions
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   Bibliography
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   List of publications