Information topologies on non-commutative state spaces

摘要: We define an information topology (I-topology) and a reverse (rI-topology) on the state space of C*-subalgebra Mat(n,C) in terms sequential convergence with respect to relative entropy. Open disks entropy base for topology. This was not evident since Csiszar has shown 1960's that analogue is wrong probability measures countably infinite set. The I-topology strictly finer than norm topology, it disconnects convex into its faces. rI-topology intermediate allows complete two fundamental theorems geometry full space, by taking closure rI-topology. can be too coarse this aim but commutative algebras equals rI-topology, so difference belongs domain quantum theory. apply our results maximization von Neumann under linear constraints correlations.