A Bell pair in a generic random matrix environment

Two non-interacting qubits are coupled to an environment. Both coupling and environment are represented by random matrix ensembles. The initial state of the pair is a Bell state, though we also consider arbitrary pure states. Decoherence of the pair is evaluated analytically in terms of purity; Monte Carlo calculations confirm these results and also yield the concurrence of the pair. Entanglement within the pair accelerates decoherence. Numerics display the relation between concurrence and purity known for Werner states, allowing us to give a formula for concurrence decay.