Entropy and optimal decompositions of states relative to a maximal commutative subalgebra
Abstract
Description
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra is a subfactor. I consider some general properties, valid for these definitions in finite dimensions, and apply them to a maximal commutative subalgebra of a full matrix algebra. The main method is an interplay between convexity and symmetry. A collection of helpful tools from convex analysis for the problems in question is collected in an appendix.
20 pages, latex, no figures. Some calculations and reasonings are done in more detail. I have to thank an unknown referee for asking me to do so. Misprints, if detected, are corrected. To be published in: Open Systems & Information Dynamics
20 pages, latex, no figures. Some calculations and reasonings are done in more detail. I have to thank an unknown referee for asking me to do so. Misprints, if detected, are corrected. To be published in: Open Systems & Information Dynamics