Entanglement of a 2-qubit system coupled to a bath of quantum spin glass

We study the quantum entanglement (concurrence) of a 2-qubit system coupled to a small spin glass bath of 2 to n ≥ 4 qubits. The bath is described by the quantum X X Heisenberg model with random J coupling and varying magnetic field h . We look at the dynamics of the steady state average concurrence for the system and obtain a general formula to describe the concurrence with J = 0 and h = 0 for n bath sites. The physics of 2-qubit system coupled with n bath sites for J = 0 is analytically described for small n . The result for large n was numerically found to be qualitatively similar. For small fluctuation in J , a mean steady state average concurrence of about 0.5 is obtained.