Secret Keys Assisted Private Classical Communication Capacity over Quantum Channels

We prove a regularized formula for the secret key-assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity cite{DHW05RI}. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes private classical communication it{without} secret key assistance as a child protocol.