Bell-type inequalities for systems of relativistic vector bosons

We perform a detailed analysis of the possi-ble 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 iden-tify two distinct classes of such states, and determine the joint probabilities of spin mea-surement outcomes for each them. We calcu-late the expectation values of the CHSH, Mer -min 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.