Temporal Quantum Correlations and Hidden Variable Models

Nonfiction, Science & Nature, Science, Physics, Quantum Theory, Computers, Advanced Computing, Information Technology
Cover of the book Temporal Quantum Correlations and Hidden Variable Models by Costantino Budroni, Springer International Publishing
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Author: Costantino Budroni ISBN: 9783319241692
Publisher: Springer International Publishing Publication: October 22, 2015
Imprint: Springer Language: English
Author: Costantino Budroni
ISBN: 9783319241692
Publisher: Springer International Publishing
Publication: October 22, 2015
Imprint: Springer
Language: English

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.

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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.

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