Temporal Quantum Correlations and Hidden Variable Models

In this thesis, the main approach to the characterization of the set of classical probabilities, the correlation polytope approach, is reviewed for different scenarios, namely, hidden variable models discussed by Bell (local), Kochen and Specker (non-contextual), and Leggett and Garg (macrorealist). Computational difficulties associated with the method are described and a method to overcome them in several nontrivial cases is presented. For the quantum case, a general method to analyze quantum correlations in the sequential measurement scenario is provided, which allows computation of the maximal correlations.

Such a method has a direct application for computation of maximal quantum violations of Leggett-Garg inequalities and it is relevant in the analysis of non-contextuality tests. Finally, possible applications of the results for quantum information tasks are discussed.

Selected for the 2015 Dissertation-Prize Symposium of the German Physical Society Nominated as an outstanding PhD Thesis by the University of Siegen Accessible pedagogical presentation for newcomers to quantum foundations Contains a concise and self-contained review of the most recent advances on the hidden variable problem and foundations of quantum mechanics Includes supplementary material: sn.pub/extras

Inhalt

Introduction.- Preliminary notions.- Noncontextuality inequalities from variable elimination.- Optimal tests for state-independent contextuality.- Quantum bounds for temporal correlations.- Dimension witnesses.- Conclusions.