Public and private communication with a quantum channel and a secret key

We consider using a secret key and a noisy quantum channel to generate noiseless public communication and noiseless private communication. The optimal protocol for this setting is the publicly enhanced private father protocol. This protocol exploits random coding techniques and “piggybacking” of public information along with secret-key-assisted private codes. The publicly enhanced private father protocol is a generalization of the secret-key-assisted protocol of Hsieh, Luo, and Brun and a generalization of a protocol for simultaneous communication of public and private information suggested by Devetak and Shor.