Resolvability of classical-quantum channels

TL;DR

This paper investigates the resolvability of classical-quantum channels, establishing new bounds and results for both worst-input and fixed-input scenarios using hypothesis testing, identification codes, and quantum Sanov theorem.

Contribution

It provides the first comprehensive analysis of classical-quantum channel resolvability for both worst-input and fixed-input cases, including strong converse results.

Findings

Derived the direct part for worst-input resolvability from sequential hypothesis testing.

Established the strong converse for worst-input resolvability via identification codes.

Solved the strong converse for fixed-input resolvability using the quantum Sanov theorem.

Abstract

Channel resolvability concerns the minimum resolution for approximating the channel output. We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and form the fixed independent and identically distributed (i.i.d.) input. The direct part of the worst-input setting is derived from sequential hypothesis testing as it involves of non-i.i.d.~inputs. The strong converse of the worst-input setting is obtained via the connection to identification codes. For the fixed-input setting, while the direct part follows from the known quantum soft covering result, we exploit the recent alternative quantum Sanov theorem to solve the strong converse.