Quantum entropy-typical subspace and universal data compression

TL;DR

This paper introduces the quantum entropy-typical subspace concept, demonstrating its ability to approximately preserve mixed states with bounded von Neumann entropy, leading to a universal quantum data compression scheme.

Contribution

It formalizes the quantum entropy-typical subspace and shows its application in universal quantum data compression for sources with entropy up to a certain threshold.

Findings

Mixed states with entropy less than h can be preserved by the entropy-typical subspace.

The entropy-typical subspace enables a universal compression scheme.

The scheme is effective for sources with von Neumann entropy not exceeding h.

Abstract

The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal compression scheme for the case that the von Neumann entropy of the source does not exceed h.