# Optimality in Quantum Data Compression using Dynamical Entropy

## TL;DR

This paper explores lossless quantum data compression for general quantum state sequences, establishing that optimal compression length equals the quantum dynamical entropy of an associated quantum Markov chain.

## Contribution

It introduces quantum stochastic ensembles and links the optimal compression length to quantum dynamical entropy, extending previous i.i.d. assumptions.

## Key findings

- Optimal average codeword length equals quantum dynamical entropy.
- Quantum stochastic ensembles generalize i.i.d. models.
- Provides a theoretical foundation for quantum data compression.

## Abstract

In this article we study lossless compression of strings of pure quantum states of indeterminate-length quantum codes which were introduced by Schumacher and Westmoreland. Past work has assumed that the strings of quantum data are prepared to be encoded in an independent and identically distributed way. We introduce the notion of quantum stochastic ensembles, allowing us to consider strings of quantum states prepared in a more general way. For any identically distributed quantum stochastic ensemble we define an associated quantum Markov chain and prove that the optimal average codeword length via lossless coding is equal to the quantum dynamical entropy of the associated quantum Markov chain.