Beware of Greeks bearing entanglement? Quantum covert channels, information flow and non-local games

TL;DR

This paper demonstrates that quantum entanglement can enhance the capacity of classical covert channels under active adversaries, introduces an algorithm to bound this capacity, and explores the undecidability of the problem.

Contribution

It reveals that entanglement can increase classical covert channel capacity and provides a semi-definite hierarchy-based method to bound this capacity.

Findings

Entanglement can increase classical covert channel capacity.

Zero-capacity channels are not improved by entanglement.

The capacity determination problem is undecidable, but an upper-bound algorithm exists.

Abstract

Can quantum entanglement increase the capacity of (classical) covert channels? To one familiar with Holevo's Theorem it is tempting to think that the answer is obviously no. However, in this work we show: quantum entanglement can in fact increase the capacity of a classical covert channel, in the presence of an active adversary; on the other hand, a zero-capacity channel is not improved by entanglement, so entanglement cannot create `purely quantum' covert channels; the problem of determining the capacity of a given channel in the presence of entanglement is undecidable; but there is an algorithm to bound the entangled capacity of a channel from above, adapted from the semi-definite hierarchy from the theory of non-local games, whose close connection to channel capacity is at the core of all of our results.