Metric adjusted skew information

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Metric adjusted skew information. / Hansen, Frank.

I: Proceedings of the National Academy of Science of the United States of America, Bind 105, Nr. 29, 2008, s. 9909-9916.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Hansen, F 2008, 'Metric adjusted skew information', Proceedings of the National Academy of Science of the United States of America, bind 105, nr. 29, s. 9909-9916. https://doi.org/10.1073/pnas.0803323105

APA

Hansen, F. (2008). Metric adjusted skew information. Proceedings of the National Academy of Science of the United States of America, 105(29), 9909-9916. https://doi.org/10.1073/pnas.0803323105

Vancouver

Hansen F. Metric adjusted skew information. Proceedings of the National Academy of Science of the United States of America. 2008;105(29):9909-9916. https://doi.org/10.1073/pnas.0803323105

Author

Hansen, Frank. / Metric adjusted skew information. I: Proceedings of the National Academy of Science of the United States of America. 2008 ; Bind 105, Nr. 29. s. 9909-9916.

Bibtex

@article{3659e800679611dd8d9f000ea68e967b,
title = "Metric adjusted skew information",
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 {"}¿-skew information,{"} parametrized by a ¿ ¿ (0, 1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations.",
author = "Frank Hansen",
note = "JEL classification: C02",
year = "2008",
doi = "10.1073/pnas.0803323105",
language = "English",
volume = "105",
pages = "9909--9916",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
publisher = "The National Academy of Sciences of the United States of America",
number = "29",

}

RIS

TY - JOUR

T1 - Metric adjusted skew information

AU - Hansen, Frank

N1 - JEL classification: C02

PY - 2008

Y1 - 2008

N2 - 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 "¿-skew information," parametrized by a ¿ ¿ (0, 1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations.

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

U2 - 10.1073/pnas.0803323105

DO - 10.1073/pnas.0803323105

M3 - Journal article

C2 - 18635683

VL - 105

SP - 9909

EP - 9916

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 29

ER -

ID: 5449044