A Multi-Sender Decoupling Theorem And Simultaneous Decoding For The Quantum Mac

In this work, we prove a novel one-shot 'multisender' decoupling theorem generalising Dupuis' seminal single sender decoupling theorem. We start off with a multipartite quantum state, say on A(1)A(2)R, where A(1), A(2) are treated as the two 'sender' systems and R is the reference system. We apply independent Haar random unitaries in tensor product on A(l) and A(2) and then send the resulting systems through a quantum channel. We want the channel output B to be almost in tensor with the untouched reference R. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard et al. [20] in the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.