Title: One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach,
Abstract: Capacity of a quantum channel characterizes the limits of reliable
communication through a noisy quantum channel. This fundamental information
theoretic question is very well studied specially in the setting of many
independent uses of the channel. An important scenario, both from practical and
conceptual point of view, is when the channel can be used only once. This is
known as the one-shot channel coding problem. We provide a tight
characterization of the one-shot entanglement assisted classical capacity of a
quantum channel. We arrive at our result by introducing a simple decoding
technique which we refer to as position-based decoding. We also consider two
other important quantum network scenarios: quantum channel with a jammer and
quantum broadcast channel. For these problems, we use the recently introduced
convex split technique [Anshu, Devabathini and Jain 2014] in addition to
position based decoding. Our approach exhibits that the simultaneous use of
these two techniques provides a uniform and conceptually simple framework for
designing communication protocols for quantum networks.