Explicit solutions for negative-probability measures for all entangled states

Abstract

We obtain explicit solutions for probability measures that reproduce quantum mechanical predictions for some spin-measurement directions for all entangled states. The necessity of negative probability in this case is shown. This constitutes another proof of Gisin's theorem that all entangled states are incompatible with any local hidden-variable models (all entangled states can violate Bell's inequality). A degree of freedom that remains in the solution is noted.