Lossless Quantum Prefix Compression for Communication Channels that are Always Open

TL;DR

This paper introduces a lossless quantum prefix compression method for unknown sources, optimizing the maximal length of quantum strings to improve communication reliability over always-open channels.

Contribution

It generalizes prefix-free quantum coding to indeterminate-length strings and presents a communication model for lossless transmission, reducing errors in noisy channels.

Findings

Achieves minimal expected maximal length of quantum strings

Extends prefix-free quantum codes to indeterminate-length strings

Provides a model for lossless quantum communication over noisy channels

Abstract

We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length of a quantum string is the maximal length in the superposition). This complements work by Schumacher and Westmoreland who calculated the corresponding rate for minimizing the output's average length. Our compressed code words are prefix-free indeterminate-length quantum bit strings which can be concatenated in the case of multiple sources. Therefore, we generalize the known theory of prefix-free quantum codes to the case of strings with indeterminate length. Moreover, we describe a communication model which allows the lossless transmission of the compressed code words. The benefit of compression is then the reduction of transmission errors in the presence of noise.