Entropy of a subalgebra and quantum estimation

In this paper we compare the accessible information of quantum communication channels with the entropic content of finite-dimensional matrix algebras with respect to quantum states, as defined by Connes, Narnhofer, and Thining. In particular, every Abelian n x n matrix algebra together with a density matrix define the input alphabet of a quantum communication channel whose accessible information equals the entropic content of the algebra with respect to the state. The cases n = 2 and n = 3 are concretely examined in connection with the problem of the best estimation. (C) 1996 American Institute of Physics.