  Two-qubit operations may be characterized by their capacities for
communication, both with and without free entanglement, and their capacity for
creating entanglement. We establish a set of inequalities that give an ordering
to the capacities of two-qubit unitary operations. Specifically, we show that
the capacities for entanglement creation and bidirectional communication
without entanglement assistance are at least as great as half the bidirectional
communication capacity with entanglement assistance. In addition, we show that
the bidirectional communication that can be performed using an ensemble may be
increased via a two-qubit unitary operation by twice the operation's capacity
for entanglement.

Quantum Physics