Classical Feedback in a Quantum Network

We study classical feedback in network communication from multiple transmitters to a single receiver over a shared quantum channel medium, where the transmitters' signals may interfere with one another. The information-theoretic model is referred to as a quantum multiple access channel (MAC) with classical feedback. Since the no-cloning theorem forbids perfect copying of the received signal, feedback is generated through measurement. The transmitters receive the feedback messages upon delay, and adapt their future transmissions accordingly. 

In general, there is a tradeoff between the transmission rates of interfering transmitters. We establish an achievable rate region for a two-user MAC, characterizing the set of rates simultaneously attainable by both users. In our code construction, each transmitter partially decodes information of the other transmitter using the feedback. In the analysis, we combine quantum information-theoretic tools with classical feedback techniques. We demonstrate our results through the quantum binary adder, which is particularly relevant to optical communication, where photons from different sources can be confused with one another. We demonstrate that feedback enables cooperation and a boost in achievable transmission rates.