Sending entanglement through noisy quantum channels.

This paper addresses some general questions of quantum information theory arising from the transmission of quantum entanglement through (possibly noisy) quantum channels. A pure entangled state is prepared of a pair of systems R and Q, after which Q is subjected to a dynamical evolution given by the superoperator $. Two interesting quantities can be defined for this process: the entanglement fidelity Fe and the entropy production Se. It turns out that neither of these quantities depends in any way on the system R, but only on the initial state and dynamical evolution of Q. Fe and Se are related to various other fidelities and entropies, and are connected by an inequality reminiscent of the Fano inequality of classical information theory. Some insight can be gained from these techniques into the security of quantum cryptographic protocols and the nature of quantum error-correcting codes.