  Recently, a coding technique called position-based coding has been used to
establish achievability statements for various kinds of classical communication
protocols that use quantum channels. In the present paper, we apply this
technique in the entanglement-assisted setting in order to establish lower
bounds for error exponents, lower bounds on the second-order coding rate, and
one-shot lower bounds. We also demonstrate that position-based coding can be a
powerful tool for analyzing other communication settings. In particular, we
reduce the quantum simultaneous decoding conjecture for entanglement-assisted
or unassisted communication over a quantum multiple access channel to open
questions in multiple quantum hypothesis testing. We then determine achievable
rate regions for entanglement-assisted or unassisted classical communication
over a quantum multiple-access channel, when using a particular quantum
simultaneous decoder. The achievable rate regions given in this latter case are
generally suboptimal, involving differences of Renyi-2 entropies and
conditional quantum entropies.
