| Popis: |
In this work, we prove a novel one-shot ‘multi-sender’ 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 $A_{1}$ 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. |
