Quantum Data Compression and Relative Entropy Revisited

TL;DR

This paper revisits quantum data compression, providing a simple proof of the role of relative entropy in quantum settings by linking quantum and classical data compression techniques.

Contribution

It offers a constructive proof connecting quantum and classical data compression codes, extending classical results to quantum information theory.

Findings

Quantum relative entropy measures non-optimality in quantum data compression.

Quantum data compression can be effectively reduced to classical data compression.

Classical information theory results are applicable to quantum data compression.

Abstract

B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide an alternative, simple and constructive proof of this result by constructing quantum compression codes (schemes) from classical data compression codes. Moreover, as the quantum data compression/coding task can be effectively reduced to a (quasi-)classical one, we show that relevant results from classical information theory and data compression become applicable and therefore can be extended to the quantum domain.