Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
Quantum Physics
2007-07-16 v3 Information Theory
Mathematical Physics
Dynamical Systems
math.IT
math.MP
Abstract
In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.
Keywords
Cite
@article{arxiv.quant-ph/0506080,
title = {Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem},
author = {Fabio Benatti and Tyll Krueger and Markus Mueller and Rainer Siegmund-Schultze and Arleta Szkola},
journal= {arXiv preprint arXiv:quant-ph/0506080},
year = {2007}
}
Comments
26 pages, no figures. Reference to publication added: published in the Communications in Mathematical Physics (http://www.springerlink.com/content/1432-0916/)