2006/07/31 by Frank Hansen · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #math-ph #math.MP
paper · pdf · doi:10.1073/pnas.0803323105
published as Proc. Natl. Acad. Sci. USA 105, 9909-9916 (2008) · Edited the abstract and the introduction
arxiv created 2008/02/21 · openalex publication_date 2008/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.