Privacy Amplification Against Quantum Side Information Via Regular Random Binning

TL;DR

This paper develops a new method for privacy amplification against quantum side information using regular random binning, providing error bounds and solving an open problem in quantum wiretap channel secrecy exponents.

Contribution

It introduces a novel approach linking privacy amplification with quantum soft covering, deriving error exponents for quantum sources and wiretap channels.

Findings

Derived error exponent and strong converse bounds for quantum sources.

Recovered known results for i.i.d. sources via type decomposition.

Established an achievable secrecy exponent for quantum wiretap channels.

Abstract

We consider privacy amplification against quantum side information by using regular random binning as an effective extractor. For constant-type sources, we obtain error exponent and strong converse bounds in terms of the so-called quantum Augustin information. Via type decomposition, we then recover the error exponent for independent and identically distributed sources proved by Dupuis [arXiv:2105.05342]. As an application, we obtain an achievable secrecy exponent for classical-quantum wiretap channel coding in terms of the Augustin information, which solves an open problem in [IEEE Trans.~Inf.~Theory, 65(12):7985, 2019]. Our approach is to establish an operational equivalence between privacy amplification and quantum soft covering; this may be of independent interest.