Entropy and algorithmic complexity in quantum information theory

A theorem of Brudno says that the entropy production of classical ergodic information sources equals the algorithmic complexity per symbol of almost every sequence emitted by such sources. The recent advances in the theory and technology of quantum information raise the question whether a same relation may hold for ergodic quantum sources. In this paper, we discuss a quantum generalization of Brudno’s result which connects the von Neumann entropy rate and a recently proposed quantum algorithmic complexity.