A unitary interaction coupling two parties enables quantum communication in
both the forward and backward directions.
Each communication capacity can be thought of as a tradeoff between the
achievable rates of specific types of forward and backward communication.
Our first result shows that for any bipartite unitary gate, coherent
classical communication is no more difficult than classical communication --
they have the same achievable rate regions. Previously this result was known
only for the unidirectional capacities (i.e., the boundaries of the tradeoff).
We then relate the tradeoff curve for two-way coherent communication to the
tradeoff for two-way quantum communication and the tradeoff for coherent
communiation in one direction and quantum communication in the other.Comment: 11 pages, v2 extensive modification and rewriting of the main proof,
v3 published version with only a few more change
