The Classical-Quantum Multiple Access Channel with Conferencing Encoders and with Common Messages

We prove coding theorems for two scenarios of cooperating encoders for the multiple access channel with two classical inputs and one quantum output. In the first scenario (ccq-MAC with common messages), the two senders each have their private messages, but would also like to transmit common messages. In the second scenario (ccq-MAC with conferencing encoders), each sender has its own set of messages, but they are allowed to use a limited amount of noiseless classical communication amongst each other prior to encoding their messages. This conferencing protocol may depend on each individual message they intend to send. The two scenarios are related to each other not only in spirit - the existence of near-optimal codes for the ccq-MAC with common messages is used for proving the existence of near-optimal codes for the ccq-MAC with conferencing encoders.