Abstract:

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, the quantum multiple-access channel, the quantum channel with a 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 study (A. Anshu, R. Jain, and N. Warsi, https://ieee.org/document/8399830). 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 the work of W. Matthews and S. Wehner, IEEE Trans. Inf. Theory 60, 7317–7329 (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.