  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.
