  We study the problem of transmission of classical messages through a quantum
channel in several network scenarios in the one-shot setting. We consider both
the entanglement assisted and unassisted cases for the point to point quantum
channel, quantum multiple-access channel, quantum channel with state and the
quantum broadcast channel. We show that it is possible to near-optimally
characterize the amount of communication that can be transmitted in these
scenarios, using the position-based decoding strategy introduced in a prior
work [Anshu, Jain and Warsi, 2017]. In the process, we provide a short and
elementary proof of the converse for entanglement-assisted quantum channel
coding in terms of the quantum hypothesis testing divergence (obtained earlier
in [Matthews and Wehner, 2014]). Our proof has the additional utility that it
naturally extends to various network scenarios mentioned above. Furthermore,
none of our achievability results require a simultaneous decoding strategy,
existence of which is an important open question in quantum Shannon theory.
