Joint Operator Algebra and QMATH Seminar

Speaker:  Mary Beth Ruskai (University of Vermont)

Title: Contraction Coefficients for Noisy Quantum Channels: Part III

Abstract: Generalized relative entropy, monotone Riemannian metrics, and geodesic distance are all known to decrease under the action of quantum channels. In the classical setting the maximal contraction rate of these is independent of the defining function and equal to the maximal contraction of the Fisher information under column stochastic matrices. Analysis of a simple CQ channel for qubits shows that the maximal contraction depends on the operator convex function used in the definition, and allows resolution of several conjectures. We also discuss bounds on, and relationships between, the maximal contraction for these quantities as well as the trace distance. This will be a continuation of seminars given in Copenhagen circa 1999 and 2010. However, for the benefit of those not in attendance then it will begin with an overview.

Based on joint work with F. Hiai.