The quantum capacity of channels with arbitrarily correlated noise

TL;DR

This paper establishes bounds on the one-shot quantum capacity of channels with arbitrarily correlated noise, enabling the calculation of quantum capacity in the asymptotic limit and connecting to known results in the memoryless case.

Contribution

It provides the first bounds on the one-shot quantum capacity for channels with correlated noise, extending quantum capacity analysis beyond memoryless channels.

Findings

Derived bounds on one-shot quantum capacity for arbitrary channels

Reduced results to known quantum capacity expressions in the memoryless case

Enabled calculation of quantum capacity with correlated noise in the asymptotic limit

Abstract

We study optimal rates for quantum communication over a single use of a channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. The corresponding capacity is often referred to as the one-shot quantum capacity. In this paper, we prove bounds on the one-shot quantum capacity of an arbitrary channel. This allows us to compute the quantum capacity of a channel with arbitrarily correlated noise, in the limit of asymptotically many uses of the channel. In the memoryless case, we explicitly show that our results reduce to known expressions for the quantum capacity.