Quantum entropy and complexity
Information Theory
2018-04-23 v1 Dynamical Systems
math.IT
Quantum Physics
Abstract
We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs~\cite{Gacs} and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A.A. Brudno~\cite{Brudno}. On the other hand, using the quantum Shannon-Mc Millan theorem~\cite{BSM}, we show that such an equality holds densely in the case of ergodic quantum spin chains.
Cite
@article{arxiv.1705.09449,
title = {Quantum entropy and complexity},
author = {Fabio Benatti and Samad Khabbazi Oskouei and Ahmad Shafiei Deh Abad},
journal= {arXiv preprint arXiv:1705.09449},
year = {2018}
}