  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.
