Bell-type inequalities for systems of relativistic vector bosons

Alan J. Barr1, Paweł Caban2, and Jakub Rembieliński2

1Department of Physics, Keble Road, University of Oxford, OX1 3RH and Merton College, Merton Street, Oxford, OX1 4JD
2Department of Theoretical Physics, University of Łódź, Pomorska 149/153, PL-90-236 Łódź, Poland

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We perform a detailed analysis of the possible violation of various Bell-type inequalities for systems of vector boson-antiboson pairs. Considering the general case of an overall scalar state of the bipartite system, we identify two distinct classes of such states, and determine the joint probabilities of spin measurement outcomes for each them. We calculate the expectation values of the CHSH, Mermin and CGLMP inequalities and find that while the generalised CHSH inequality is not expected to be violated for any of the scalar states, in the case of the Mermin and CGLMP inequalities the situation is different – these inequalities can be violated in certain scalar states while they cannot be violated in others. Moreover, the degree of violation depends on the relative speed of the two particles.

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