Decoherence can help quantum cryptographic security

In quantum key distribution, one conservatively assumes that the eavesdropper Eve is restricted only by physical laws, whereas the legitimate parties, namely the sender Alice and receiver Bob, are subject to realistic constraints, such as noise due to environment-induced decoherence. In practice, Eve too may be bound by the limits imposed by noise, which can give rise to the possibility that decoherence works to the advantage of the legitimate parties. A particular scenario of this type is one where Eve can’t replace the noisy communication channel with an ideal one, but her eavesdropping channel itself remains noiseless. Here, we point out such a situation, where the security of the ping–pong protocol (modified to a key distribution scheme) against a noise-restricted adversary improves under a non-unital noisy channel, but deteriorates under unital channels. This highlights the surprising fact that, contrary to the conventional expectation, noise can be helpful to quantum information processing. Furthermore, we point out that the measurement outcome data in the context of the non-unital channel can’t be simulated by classical noise locally added by the legitimate users.