Applications of position-based coding to classical communication over quantum channels

We exploit a coding technique called position-based coding in the entanglement-assisted setting to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds, and 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 an achievable rate region 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-two entropies and conditional quantum entropies.