Markov invariant geometry on manifolds of states
Integrity signals
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Claims the paper makes
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
For the Wigner-Yanase metric, C(ΔHλμ,ΔHλν) reduces to the skew information between the evolved state and ΔH when μ=ν.
“CðΔH λ μ ; ΔH λ ν Þ ≔ -ð1=2ÞTrð½ ffiffiffiffi ffi ρ λ p ;ΔH λ μ ½ ffiffiffiffi ffi ρ λ p ;ΔH λ ν Þ reduces to the skew information between the evolved state and [57].”
From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [57]
The QFIM belongs to a family of contractive Riemannian metrics, associated with which the infinitesimal distance in state space is ds^2 = Σ g_μν dx^μ dx^ν with g_μν as the contractive Riemannian metric.
“In more concrete terms, the QFIM belongs to a family of contractive Riemannian metric [24,26,89,90], associated with which the infinitesimal distance in state space is ds 2 = µ g µν dx µ dx ν with g µν as the contractive Riemannian metric.”
From Quantum Fisher information matrix and multiparameter estimation (2020) · cites this paper as [89]
The citation lists haven’t been fetched yet
References 18 · Cited by 98
- Authors
- Morozova, E. A., & Chentsov, N. N.
- ORCID
- Morozova, E. A.
- Venue
- Journal of Soviet Mathematics
- Published
- 1991-10
- Volume
- 56
- Issue
- 5
- Pages
- 2648-2669
- ISSN
- 1072-3374 (ISSN-L)
- 0090-4104
- 1573-8795
- OpenAlex
- W2088655718
- Cited by
- 98
- References
- 18
- Citations by year
- 2026: 6 · 2025: 6 · 2024: 6 · 2023: 13 · 2022: 5 · 2021: 7 · 2020: 14 · 2019: 8 · 2018: 6 · 2017: 5 · 2016: 4 · 2015: 6 · 2013: 4
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Journal of Mathematical Sciences (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- Markov maps, invariant metrics, classical statistics, Riemannian metrics, geodesics, linear connections, totally geodesic submanifolds, uniform topology
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.
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