  Unitary gates are an interesting resource 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 will 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.
