Secure communication over fully quantum Gel'fand-Pinsker wiretap channel

TL;DR

This paper extends the classical Gel'fand-Pinsker wiretap channel results to the fully quantum case, providing new bounds in terms of error exponents and establishing a simultaneous decoder for secure quantum communication.

Contribution

It generalizes classical results to the quantum setting, introduces a simultaneous decoding technique, and proves new resolvability lemmas for secure quantum communication.

Findings

Achievable rate bounds in terms of error exponents.

Existence of a simultaneous decoder for the quantum channel.

Achievable rate for the quantum Gel'fand-Pinsker channel without Eve.

Abstract

In this work we study the problem of secure communication over a fully quantum Gel'fand-Pinsker channel. The best known achievability rate for this channel model in the classical case was proven by Goldfeld, Cuff and Permuter in [Goldfeld, Cuff, Permuter, 2016]. We generalize the result of [Goldfeld, Cuff, Permuter, 2016]. One key feature of the results obtained in this work is that all the bounds obtained are in terms of error exponent. We obtain our achievability result via the technique of simultaneous pinching. This in turn allows us to show the existence of a simultaneous decoder. Further, to obtain our encoding technique and to prove the security feature of our coding scheme we prove a bivariate classical-quantum channel resolvability lemma and a conditional classical-quantum channel resolvability lemma. As a by product of the achievability result obtained in this work, we also obtain an achievable rate for a fully quantum Gel'fand-Pinsker channel in the absence of Eve. The form of this achievable rate matches with its classical counterpart. The Gel'fand-Pinsker channel model had earlier only been studied for the classical-quantum case and in the case where Alice (the sender) and Bob (the receiver) have shared entanglement between them.