Physics – Mathematical Physics
Scientific paper
2006-07-23
Proc. Natl. Acad. Sci. USA 105, 9909-9916 (2008)
Physics
Mathematical Physics
Edited the abstract and the introduction
Scientific paper
10.1073/pnas.0803323105
We extend the concept of Wigner-Yanase-Dyson skew information to something we call ``metric adjusted skew information'' (of a state with respect to a conserved observable). This ``skew information'' is intended to be a non-negative quantity bounded by the variance (of an observable in a state) that vanishes for observables commuting with the state. We show that the skew information is a convex function on the manifold of states. It also satisfies other requirements, proposed by Wigner and Yanase, for an effective measure-of-information content of a state relative to a conserved observable. We establish a connection between the geometrical formulation of quantum statistics as proposed by Chentsov and Morozova and measures of quantum information as introduced by Wigner and Yanase and extended in this article. We show that the set of normalized Morozova-Chentsov functions describing the possible quantum statistics is a Bauer simplex and determine its extreme points. We determine a particularly simple skew information, the ``lambda-skew information,'' parametrized by a lambda in (0,1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations. Key words: Skew information, convexity, monotone metric, Morozova-Chentsov function, lambda-skew information.
No associations
LandOfFree
Metric adjusted skew information does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Metric adjusted skew information, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metric adjusted skew information will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-137448