CoChat
Sign Up
Cited by 105Quantum Mechanics and ApplicationsMathematical Inequalities and ApplicationsStatistical Mechanics and Entropy

Wigner–Yanase information on quantum state space: The geometric approach

Open access
Gibilisco, Paolo, Isola, Tommaso·2003·Journal of Mathematical Physics
DOI 10.1063/1.1598279
Open this paper in CoChat — free accountOpen PDF

Abstract

In the search of appropriate Riemannian metrics on quantum state space, the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by Petz. All the elements of this family of geometries can be seen as quantum analogs of Fisher information. Although there exists a number of general theorems shedding light on this subject, many natural questions, also stemming from applications, are still open. In this paper we discuss a particular member of the family, the Wigner–Yanase information. Using a well-known approach that mimics the classical pull-back approach to Fisher information, we are able to give explicit formulas for the geodesic distance, the geodesic path, the sectional and scalar curvatures associated to Wigner–Yanase information. Moreover, we show that this is the only monotone metric for which such an approach is possible.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1063/1.1598279

Cites

49 of 49 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The geodesic distance for the quantum Fisher information metric is L_QF(ρ,σ)=arccos[√F(ρ,σ)], where F is the Uhlmann fidelity.

    “L QF ðρ; σÞ ¼ arccos½ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Fðρ; σÞ p ;ð5Þ”

    From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [56]

  • Analytic expressions for geodesic distance are known only for the quantum Fisher information metric and the Wigner-Yanase information metric.

    “In fact, analytic expressions are known only for the geodesic distance related to the quantum Fisher information metric [56],”

    From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [56]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 3

  1. [22][22] Grasselli, M.R., Streater R.F., The quantum information manifold for ǫ -boundend forms. Rep. Math. Phys., 46 (3), 325-335, 2000. -
  2. [41][41] Ruskai, M. B. Contraction of riemannian metrics and related distance measures on pairs of qubit states. Preprint, 2002. -
  3. [42][42] Wigner, E., Yanase M., Information content of distribution. Proc. Nat. Acad. Sci. USA 49 , 910-918, 1963. -

Cited by

Sorted by citations

Related

Authors
Gibilisco, P., & Isola, T.
Affiliations
  • University of Chieti-Pescara (IT)
  • University of Rome Tor Vergata (IT)
ORCID
Venue
Journal of Mathematical Physics
Publisher
AIP Publishing
Published
2003-09-01
Volume
44
Issue
9
Pages
3752-3762
ISSN
  • 0022-2488 (ISSN-L)
  • 1089-7658
DOI
10.1063/1.1598279
OpenAlex
W1977745931
Cited by
105
References
49
Citations by year
2026: 1 · 2025: 7 · 2024: 6 · 2023: 8 · 2022: 4 · 2021: 3 · 2020: 7 · 2019: 6 · 2018: 6 · 2017: 5 · 2016: 9 · 2015: 2 · 2014: 1 · 2013: 2
FWCI
3.17
Type
journal article
Language
en
Open access
Locations
  • Journal of Mathematical Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Cineca Institutional Research Information System (Tor Vergata University) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
Ministero dell’Istruzione, dell’Università e della Ricerca
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Mathematics › Applied Mathematics › Mathematical Inequalities and Applications
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
Keywords
quantum state space, Riemannian metrics, Fisher information, geodesic distance, geodesic paths, sectional curvature, scalar curvature, quantum information geometry

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review