Secret Keys Assisted Private Classical Communication Capacity over Quantum Channels
Min-Hsiu Hsieh, Zhicheng Luo, and Todd Brun

TL;DR
This paper derives a regularized formula for the secret key-assisted capacity of quantum channels for private classical communication, introducing the private father protocol within the resource inequality framework.
Contribution
It presents a new capacity formula for secret key-assisted private classical communication over quantum channels and introduces the private father protocol.
Findings
Derived a regularized capacity formula for secret key-assisted communication
Introduced the private father protocol as a new resource inequality-based protocol
Established parallels with Devetak's entanglement-assisted quantum capacity
Abstract
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.
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