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arXiv:1408.6023 · Physical Review A

Time-dependent Bell inequalities in a Wigner form

N. Nikitin, V. Sotnikov, K. S. Toms

Published Oct 31, 2014• 8 citations
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Abstract

We derive a class of time-dependent Bell inequalities in Wigner form under the assumption of locality in the framework of Kolmogorov's probability theory. We consider violation of the obtained inequalities for three cases: spin correlations in an external magnetic field, oscillations of neutral pseudoscalar mesons, and decays of a pseudoscalar into a fermion-antifermion pair.

DOI
10.1103/physreva.90.042124

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We derive a class of time-dependent Bell inequalities in Wigner form under the assumption of locality in the framework of Kolmogorov's probability theory. We consider violation of the obtained inequalities for three cases: spin correlations in an external magnetic field, oscillations of neutral pseudoscalar mesons, and decays of a pseudoscalar into a fermion-antifermion pair.
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We propose time-dependent Bell inequalities in a Wigner form, which expand the possibilities of experimental verification of Bohr’s principle of complementarity in the relativistic domain and for nonstationary quantum-mechanical systems. Derivation of the proposed inequalities is based entirely on the Kolmogorov axiomatics of probability theory and the locality hypothesis. Violation of the obtained inequalities is considered in the framework of quantum theory based on the example of oscillations of neutral B mesons.
Recently a new class of time-dependent Bell inequalities in Wigner form was introduced. The structure of the inequalities allows experimental studies of quantum and open quantum systems in external fields. In this paper, we study the properties of the time-dependent Wigner inequalities using the time evolution of neutral pseudoscalar mesons with CPCPCP-violation effects taken into account. It is shown that it is always possible to find a range of parameters to test for violation in an experimentally accessible area. The effect of the relaxation of the inequalities for large time scales is demonstrated.
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In this study, we introduce the concept of classicality and derive Wigner inequalities that depend on two instants, with a potential extension to three instants. We explore the experimental feasibility of testing the violations of these inequalities in both pure and mixed flavor states of ${K}^{0}\ensuremath{-}$, D0{D}^{0}D0-, and Bs{B}_{s}Bs​- meson pairs. Using the Werner noise model, we demonstrate that violations of time-dependent Wigner inequalities can be detected even when background processes constitute up to 50% of the system.