We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation}, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard, Devetak and Hayden. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.

翻译：我们证明了在无纠缠辅助的双发送方量子多址接入信道（QMAC）和无辅助双发送方双接收方量子干扰信道（QIC）上，传输量子信息的首个非平凡单次内界。先前研究仅针对信道独立同分布多次使用的渐近极限（即渐近iid情形）下的无辅助QMAC，且完全未涉及无辅助QIC。我们采用速率分裂与连续消除两种技术以获得内界。速率分裂技术此前被用于在渐近iid设置下避免时间共享以获取经典信道的内界。本文的主要技术贡献在于将速率分裂从经典渐近iid设置推广到量子单次设置。在渐近iid极限下，我们针对QMAC的单次内界趋近于Yard、Devetak和Hayden的速率区域。针对QIC，我们在渐近iid设置下获得了新型非平凡速率区域。所有结果还可扩展至有限纠缠辅助情形，涵盖单次和渐近iid两种设置。针对QMAC和QIC的有限纠缠单次结果是全新的。对于QIC，即便在渐近iid设置下，有限纠缠结果亦是首次提出。