  Bennett et al. showed that allowing shared entanglement between a sender and
receiver before communication begins dramatically simplifies the theory of
quantum channels, and these results suggest that it would be worthwhile to
study other scenarios for entanglement-assisted classical communication. In
this vein, the present paper makes several contributions to the theory of
entanglement-assisted classical communication. First, we rephrase the
Giovannetti-Lloyd-Maccone sequential decoding argument as a more general
"packing lemma" and show that it gives an alternate way of achieving the
entanglement-assisted classical capacity. Next, we show that a similar
sequential decoder can achieve the Hsieh-Devetak-Winter region for
entanglement-assisted classical communication over a multiple access channel.
Third, we prove the existence of a quantum simultaneous decoder for
entanglement-assisted classical communication over a multiple access channel
with two senders. This result implies a solution of the quantum simultaneous
decoding conjecture for unassisted classical communication over quantum
multiple access channels with two senders, but the three-sender case still
remains open (Sen recently and independently solved this unassisted two-sender
case with a different technique). We then leverage this result to recover the
known regions for unassisted and assisted quantum communication over a quantum
multiple access channel, though our proof exploits a coherent quantum
simultaneous decoder. Finally, we determine an achievable rate region for
communication over an entanglement-assisted bosonic multiple access channel and
compare it with the Yen-Shapiro outer bound for unassisted communication over
the same channel.
