Coding for quantum channels with side information at the transmitter

TL;DR

This paper derives a single-letter formula for the entanglement-assisted quantum capacity of channels with transmitter side information, paralleling classical results, and provides bounds for unassisted capacities.

Contribution

It introduces a quantum analogue of Gel'fand and Pinsker's classical capacity formula for channels with side information at the transmitter.

Findings

Single-letter expression for entanglement-assisted quantum capacity

Lower bound on unassisted quantum capacity

Parallel to classical Gel'fand-Pinsker solution

Abstract

We consider the problem of coding for quantum channels with side information that is available ahead of time at the transmitter but not at the receiver. We find a single-letter expression for the entanglement-assisted quantum capacity of such channels which closely parallels Gel'fand and Pinsker's solution to the classical version of the same problem. This theorem can also be used to find a lower bound on the unassisted quantum capacity of these channels.