# Quantum Kolmogorov complexity and its applications

**Authors:** C. Mora, H. Briegel, B. Kraus  
**arXiv:** [quant-ph/0610109](https://arxiv.org/abs/quant-ph/0610109)  
**Date:** 2006-10-13  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/quant-ph--0610109v1/

## Key points

- Quantum Kolmogorov complexity measures information needed to describe a quantum state
- Extends classical Kolmogorov complexity to quantum mechanics
- Pure n-qubit state requires exponentially large number of bits for description
- Connection between classical communication complexity and quantum Kolmogorov complexity
- Applications in quantum computation and thermodynamics
- Extension to encompass mixed quantum states for more intricate systems

## Summary

The paper "Quantum Kolmogorov Complexity and its Applications" by C. Mora, H. Briegel, and B. Kraus delves into the concept of quantum Kolmogorov complexity as a measure of information needed to describe a quantum state. This builds upon classical Kolmogorov complexity which quantifies information in binary strings and extends it to the realm of quantum mechanics. The study reveals that regardless of how one defines quantum Kolmogorov complexity in terms of classical bits required for description, there will always exist a pure n-qubit state that demands an exponentially large number of bits for its description. This is supported by establishing a connection between classical communication complexity and quantum Kolmogorov complexity. The authors also showcase various applications of this measure in fields such as quantum computation and thermodynamics, highlighting its versatility and significance in understanding complex systems. Furthermore, the paper extends the concept to encompass mixed quantum states, making it applicable to more intricate systems. Overall, this research sheds light on fundamental aspects of information theory within the context of quantum mechanics and opens up new avenues for exploring information processing in these systems.