Abstract
The entropy of a subalgebra, which has been used in quantum ergodic theory to construct a noncommutative dynamical entropy, coincides for N-level systems and Abelian subalgebras with the notion of maximal mutual information of quantum communication theory. The optimal decompositions of mixed quantum states singled out by the entropy of Abelian subalgebras correspond to optimal detection schemes at the receiving end of a quantum channel. It is then worthwhile studying in some detail the structure of the convex hull of quantum states brought about by the variational definition of the entropy of a subalgebra. In this Letter, we extend previous results on the optimal decompositions for 3-level systems.
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