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arXiv:1503.05332 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Proposal for experimental test of the time-dependent Wigner inequalities for neutral pseudoscalar meson systems

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

Published Jul 20, 2015• 16 citations
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Abstract

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 $CP$-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.

DOI
10.1103/physrevd.92.016008

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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.
A radically new class of Bell inequalities in Wigner’s form was obtained on the basis of Kolmorov’s axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner’s form). By using these inequalities, one can propose a means for experimentally testing Bohr’ complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion–antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett–Garg approach, for example.
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 K0K^0K0-, D0D^0D0-, and BsB_sBs​- 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.
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.
The classicality concept is formulated. It is used to derive Wigner inequalities dependent on three instants. The possibility of testing experimentally violations of these inequalities in pure and mixed flavor states of a pair of neutral pseudoscalar mesons is studied. Within the Werner background model, it is shown that a violation of time-dependent Wigner inequalities may be observed even at a 50 %\%% fraction of background processes.
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.