Causal limit on quantum communication

TL;DR

This paper establishes a fundamental link between quantum causality, measured by temporal correlations, and the maximum capacity of quantum channels, providing a simpler and improved upper bound for certain noisy channels.

Contribution

It introduces a causality-based upper bound on quantum channel capacity, connecting temporal quantum correlations with communication limits, and demonstrates its effectiveness on shifted depolarizing channels.

Findings

Causality measure bounds channel capacity from above.

The new bound is easier to compute than previous bounds.

Application to shifted depolarizing channels shows improved results.

Abstract

The capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement. Analogous to entanglement, the notion of a causality measure characterises the temporal aspect of quantum correlations. Despite holding an equally fundamental role in physics, temporal quantum correlations have yet to find their operational significance in quantum communication. Here we uncover a connection between quantum causality and channel capacity. We show the amount of temporal correlations between two ends of the noisy quantum channel, as quantified by a causality measure, implies a general upper bound on its channel capacity. The expression of this new bound is simpler to evaluate than most previously known bounds. We demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels, which results in improvement over previously calculated bounds for this class of channels.