Metric adjusted skew information

Frank Hansen

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

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 "λ-skew information," parametrized by a λ ε (0, 1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations.

Original languageEnglish
Pages (from-to)9909-9916
Number of pages8
JournalProceedings of the National Academy of Sciences of the United States of America
Volume105
Issue number29
DOIs
Publication statusPublished - 2008 Jul 22

Keywords

  • Convexity
  • Monotone metric
  • Morozova-Chentsov function
  • λ-skew information

ASJC Scopus subject areas

  • General

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