Time Reversal and Exchange Symmetries of Unitary Gate Capacities

Unitary gates are interesting resources for quantum communication in part because they are always invertible and are intrinsically bidirectional. This paper explores these two symmetries: time-reversal and exchange of Alice and Bob. We present examples of unitary gates that exhibit dramatic separations between forward and backward capacities (even when the back communication is assisted by free entanglement) and between entanglement-assisted and unassisted capacities, among many others. Along the way, we will give a general time-reversal rule for relating the capacities of a unitary gate and its inverse that will explain why previous attempts at finding asymmetric capacities failed. Finally, we will see how the ability to erase quantum information and destroy entanglement can be a valuable resource for quantum communication.Engineering and Physical Sciences Research Council (grant "QIP IRC")European Commission (QAP project (Contract IST-2005-15848))National Science Foundation (U.S.) (Grant CCF-0431787: "Quantum Channel Capacities and Quantum Complexity"