Rate-Distortion Theory for Mixed States

TL;DR

This paper derives the rate-distortion function for quantum data compression of mixed states with side information, characterizing the trade-off between compression rate and error in various quantum scenarios.

Contribution

It provides the first explicit characterization of the quantum rate-distortion function for mixed states, including entanglement-assisted and unassisted cases, and introduces a comprehensive compression scheme.

Findings

Rate-distortion functions expressed via mutual information and entanglement of purification.

Full qubit-entanglement rate region derived for combined communication and entanglement use.

Compression scheme applicable to various models depending on side information structure.

Abstract

This paper is concerned with quantum data compression of asymptotically many independent and identically distributed copies of ensembles of mixed quantum states. The encoder has access to a side information system. The figure of merit is per-copy or local error criterion. Rate-distortion theory studies the trade-off between the compression rate and the per-copy error. The optimal trade-off can be characterized by the rate-distortion function, which is the best rate given a certain distortion. In this paper, we derive the rate-distortion function of mixed-state compression. The rate-distortion functions in the entanglement-assisted and unassisted scenarios are in terms of a single-letter mutual information quantity and the regularized entanglement of purification, respectively. For the general setting where the consumption of both communication and entanglement are considered, we present the full qubit-entanglement rate region. Our compression scheme covers both blind and visible compression models (and other models in between) depending on the structure of the side information system.