Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem

Details Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem

2005-06-10

arxiv.org/abs/quant-ph/0506080v3

Communications in Mathematical Physics, Vol. 265, No.2 / July 2006, 437-461

Physics

Quantum Physics

26 pages, no figures. Reference to publication added: published in the Communications in Mathematical Physics (http://www.sp

Scientific paper

10.1007/s00220-006-0027-z

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.

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