Bidirectional coherent classical communication

A unitary interaction coupling two parties enables quantum or classical 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, bidirectional coherent classical communication is no more difficult than bidirectional 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 for two-way coherent communication to the tradeoff for two-way quantum communication and the tradeoff for coherent communication in one direction and quantum communication in the other