Beware of Greeks bearing entanglement? Quantum covert channels, information flow and non-local games
This addresses fundamental limitations in quantum information theory for researchers in cryptography and quantum computing, with foundational implications.
The authors investigated whether quantum entanglement can increase the capacity of classical covert channels, finding that it can do so in the presence of an active adversary but cannot create purely quantum channels from zero-capacity ones, and they proved the problem of determining this capacity is undecidable while providing an algorithm to bound it.
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.