Spin bath decoherence of quantum entanglement

We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein–Podolsky–Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one bath and two bath cases, we find that while two of the Bell states always obey the inequality, the other two violate the inequality at early times.