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We determine the secrecy capacities of AVQCs (arbitrarily varying quantumchannels). Both secrecy capacity with average error probability and withmaximal error probability are derived. Both derivations are based on one commoncode construction. The code we construct fulfills a stringent secrecyrequirement, which is called the strong code concept. We determine when thesecrecy capacity is a continuous function of the system parameters andcompletely characterize its discontinuity points both for average errorcriterion and for maximal error criterion. Furthermore, we prove the phenomenon"super-activation" for secrecy capacities of AVQCs, i.e., two quantum channelsboth with zero secrecy capacity, which, if used together, allow securetransmission with positive capacity. We also discuss the relations between theentanglement distillation capacity, the entanglement generating capacity, andthe strong subspace transmission capacity for AVQCs.

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