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Entropy and Algorithmic Complexity in Quantum Information Theory: a Quantum Brudno's Theorem

Fabio Benatti, Tyll Krueger, Markus Mueller, Rainer Siegmund-Schultze, Arleta Szkola

35 pages, no figures
License: not stated (all rights reserved)

Abstract: In classical information theory, entropy rate and algorithmic 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 algorithmic complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.

Submitted to arXiv on 10 Jun. 2005