Abstract

July 4 - 14.30-15.20
M. B. Ruskai - Monotone Metrics on Density Matrices

The distance between two density matrices in quantum information theory can be measured in many ways, including the trace norm, the relative entropy (which is not a true metric) and the Bures metric. All of these contract under completely positive, trace-preserving maps. We describe a general framework for monotone metrics using convex operator functions. Each function in the class defines a symmetric relative entropy pseudo-distance, a Riemannian metric on the tangent space, and a geodesic distance.

[Contraction of Relative Entropy, Riemannian Metrics and Related Measures of Distance between States on Non-commutative Probability Spaces (PDF)]

[Examples of monotone metrics and related quantities (PDF)] [an error occurred while processing this directive]