# Quantum Data Compression and Relative Entropy Revisited

**Authors:** Alexei Kaltchenko  
**arXiv:** [0805.0328](https://arxiv.org/abs/0805.0328)  
**Date:** 2008-05-02  
**Summary page:** https://www.summarizepaper.com/en/paper/0805.0328v2/

## Key points

- Authors explore the relationship between classical and quantum data compression
- They build upon the work of Schumacher and Westmoreland regarding relative entropy in classical data compression
- Authors provide an alternative proof by constructing quantum compression codes using classical data compression codes
- This approach demonstrates the connection between classical and quantum data compression
- Task of quantum data compression can be effectively reduced to a quasi-classical one
- Relevant results from classical information theory and data compression can be applied to the quantum domain
- Extending principles from classical to quantum systems contributes to understanding of both fields
- Paper presents a refined perspective on the relationship between classical and quantum data compression

## Summary

In their paper titled "Quantum Data Compression and Relative Entropy Revisited," authors B. Schumacher, M. Westmoreland, and Alexei Kaltchenko explore the relationship between classical and quantum data compression. They build upon the work of Schumacher and Westmoreland who established a quantum analog of a well-known classical information theory result regarding the role of relative entropy as a measure of non-optimality in classical data compression. The authors provide an alternative proof of this result by constructing quantum compression codes (schemes) using classical data compression codes. This approach offers simplicity and constructiveness in demonstrating the connection between classical and quantum data compression. Furthermore, the authors show that the task of quantum data compression can be effectively reduced to a quasi-classical one. This reduction allows them to apply relevant results from classical information theory and data compression to the quantum domain. By extending these principles to quantum systems, they contribute to our understanding of how classical concepts can be adapted for use in quantum information processing. Overall, this paper presents a refined perspective on the relationship between classical and quantum data compression. Through their alternative proof and reduction techniques, the authors demonstrate how ideas from classical information theory can be applied in the context of quantum systems, paving the way for further advancements in both fields.