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In this work, we prove a novel one-shot multi-sender decoupling theoremgeneralising Dupuis result. We start off with a multipartite quantum state, sayon A1 A2 R, where A1, A2 are treated as the two sender systems and R is thereference system. We apply independent Haar random unitaries in tensor producton A1 and A2 and then send the resulting systems through a quantum channel. Wewant the channel output B to be almost in tensor with the untouched referenceR. Our main result shows that this is indeed the case if suitable entropicconditions are met. An immediate application of our main result is to obtain aone-shot simultaneous decoder for sending quantum information over a k-senderentanglement unassisted quantum multiple access channel (QMAC). The rate regionachieved by this decoder is the natural one-shot quantum analogue of thepentagonal classical rate region. Assuming a simultaneous smoothing conjecture,this one-shot rate region approaches the optimal rate region of Yard, Dein theasymptotic iid limit. Our work is the first one to obtain a non-trivialsimultaneous decoder for the QMAC with limited entanglement assistance in bothone-shot and asymptotic iid settings; previous works used unlimitedentanglement assistance.

One-shot multi-sender decoupling and simultaneous decoding for the quantum MAC