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 Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.
In REF , a quantum version of Brudno's theorem is proven, connecting the Von Neumann entropy rate and two notions of quantum Kolmogorov complexity.
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
Communications in Mathematical Physics, Vol. 265, No.2 / July 2006, 437-461
Mathematics Physics Computer Science