Quantum dynamical entropy from Relative entropy

Details Quantum dynamical entropy from Relative entropy Quantum dynamical entropy from Relative entropy

2007-01-06

arxiv.org/abs/math/0701186v2

Mathematics

Operator Algebras

This paper is an enlarged version of my talk at Indian Statistical Institute 2001 and v2 includes some correction but no new r

Scientific paper

In this exposition we prove an existence theorem for a quantum mechanical dynamical entropy based on von-Neumann's measurement theory. To that end we introduced a Shannon type of information associated with a quantum channel or measurement based on Araki's relative entropy. This is an invariance for the dynamics which generalizes Kolmogorov-Sinai 's notion of dynamical entropy of a measure preserving transformation. In this context we also introduce a natural notion of channel capacity as a generalization of Shannon's capacity of a channel and finds its relation with A.S. Holevo's notion of capacity.

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