Relations for classical communication capacity and entanglement capability of two-qubit operations

Bipartite operations underpin both classical communication and entanglement generation. Using a superposition of classical messages, we show that the capacity of a two-qubit operation for error-free entanglement-assisted bidirectional classical communication cannot exceed twice the entanglement capability. In addition, we show that any bipartite two-qubit operation can increase the communication that may be performed using an ensemble by twice the entanglement capability.