One-shot inner bounds for quantum multiple-access one-time pad

We consider the one-shot coding of multiple access channels one-time pad. Suppose that the senders and the receiver share an entangled state in the multi-party systems. Using the position-based coding, each sender encodes the classical messages on their systems, then they transmit their systems over the ideal quantum channels. The receiver applies a decoding operator to all the systems in order to figure out which message was transmitted with respect to the quantum joint typicality lemma. We provide the upper bound of the information leakage by the convex split lemma. Combining quantum max-information with quantum hypothesis testing mutual information, we give the inner bound of the achievable rate.