Duality Between Source Coding With Quantum Side Information and Classical-Quantum Channel Coding
Journal
IEEE Transactions on Information Theory
Journal Volume
68
Journal Issue
11
Pages
7315
Date Issued
2022-11-01
Author(s)
Abstract
In this paper, we establish an interesting duality between two different quantum information-processing tasks, namely, classical source coding with quantum side information, and channel coding over classical-quantum channels. The duality relates the optimal error exponents of these two tasks, generalizing the classical results of Ahlswede and Dueck [IEEE Trans. Inf. Theory, 28(3):430-443, 1982]. We establish duality both at the operational level and at the level of the entropic quantities characterizing these exponents. For the latter, the duality is given by an exact relation, whereas for the former, duality manifests itself in the following sense: an optimal coding strategy for one task can be used to construct an optimal coding strategy for the other task. Along the way, we derive a bound on the error exponent for classical-quantum channel coding with constant composition codes which might be of independent interest. Finally, we consider the task of variable-length classical compression with quantum side information, and a duality relation between this task and classical-quantum channel coding can also be established correspondingly. Furthermore, we study the strong converse of this task, and show that the strong converse property does not hold even in the i.i.d. scenario.
Subjects
classical-quantum channel coding | Duality | error exponent | quantum side information | Slepian-Wolf coding | strong converse
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Type
journal article