Entanglement versus relaxation and decoherence in a quantum algorithm for quantum chaos

We study analytically and numerically the behavior of the concurrence (a measure of the entanglement of formation) of a pair of qubits in a quantum computer operating an efficient algorithm for quantum chaos. Our results show that in an ideal algorithm the entanglement decays exponentially with the diffusive relaxation rate induced by classical chaos. This decay reaches a residual level which drops exponentially with increasing number of qubits $n_q.$ Decoherence destroys the residual entanglement with a rate exponential in $n_q.$