Secret Message Transmission over Quantum Channels under Adversarial Quantum Noise: Secrecy Capacity and Super-Activation

We determine the secrecy capacities of arbitrarily varying quantum channels. Both secrecy capacity with average error probability and with maximal error probability are derived. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. We determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon “super-activation” for secrecy capacities of arbitrarily varying quantum channels, i.e., two quantum channels both with zero secrecy capacity, if used together, allow secure transmission with positive capacity. 1 ar X iv :1 71 2. 05 70 2v 1 [ cs .I T ] 1 4 D ec 2 01 7