2000/07/14 by Robert Schrader, Schrader, Robert
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #advanced mathematical theories #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0007020
15 pages AMS-latex, submitted for Publication to the Fields Institute Communication Series in a volume dedicated to the 60th Birthday of Sergio Doplicher and John Roberts
arxiv created 2000/07/14 · arxiv updated 2009/11/30
This article provides sufficient conditions for positive maps on the Schatten classes \mathcal Jp, 1≤ p<∞ of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on \mathcal J1, the space of trace class operators, to have a unique, strictly positive density matrix which is left invariant under the map. Conversely to any given strictly positive density matrix there are trace preserving, positive maps for which the density matrix is the unique Perron-Frobenius vector.