Two destructive effects of decoherence on Bell inequality violation
We consider a system of two spin-1/2 particles, initially in an entangled
Bell state. If one of the particles is interacting with an environment (e.g. a
collection of N independent spins), the two-particle system undergoes
decoherence. Using a simple model of decoherence, we show that this process has
two consequences. First, the maximal amount by which the CHSH inequality is
violated decays to zero. Second, the set of directions of measurement for which
the inequality is violated is reduced in the course of decoherence. The volume
of that set is bounded above by C|r|^2, where r is the decoherence factor. We
obtain similar results for the case when each of the two particles is in
interaction with a separate environment.