Publication:
From the Jordan product to Riemannian geometries on classical and quantum states

dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorCiaglia, F. M.
dc.contributor.authorJost, Jünger
dc.contributor.authorSchwachhöfer, Lorenz
dc.date.accessioned2022-05-19T12:32:23Z
dc.date.available2022-05-19T12:32:23Z
dc.date.issued2020-06-08
dc.description.abstractThe Jordan product on the self-adjoint part of a finite-dimensional C*-algebra A is shown to give rise to Riemannian metric tensors on suitable manifolds of states on A, and the covariant derivative, the geodesics, the Riemann tensor, and the sectional curvature of all these metric tensors are explicitly computed. In particular, it is proved that the Fisher-Rao metric tensor is recovered in the Abelian case, that the Fubini-Study metric tensor is recovered when we consider pure states on the algebra B(H) of linear operators on a finite-dimensional Hilbert space H, and that the Bures-Helstrom metric tensors is recovered when we consider faithful states on B(H). Moreover, an alternative derivation of these Riemannian metric tensors in terms of the GNS construction associated to a state is presented. In the case of pure and faithful states on B(H), this alternative geometrical description clarifies the analogy between the Fubini-Study and the Bures-Helstrom metric tensor.en
dc.description.statusPublicadoes
dc.format.extent27
dc.identifier.bibliographicCitationEntropy, (2020), 22(6), 637.en
dc.identifier.doihttps://doi.org/10.3390/E22060637
dc.identifier.issn1099-4300
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue6
dc.identifier.publicationlastpage27
dc.identifier.publicationtitleEntropyen
dc.identifier.publicationvolume22
dc.identifier.urihttps://hdl.handle.net/10016/34850
dc.identifier.uxxiAR/0000029184
dc.language.isoengen
dc.publisherMDPIen
dc.rights©c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherInformation geometryen
dc.subject.otherFisher–Rao metric tensoren
dc.subject.otherQuantum stateses
dc.subject.otherFubini–Study metric tensoren
dc.subject.otherBures–Helstrom metric tensoren
dc.subject.otherJordan producten
dc.subject.otherDifferential geometry of C*-algebrasen
dc.titleFrom the Jordan product to Riemannian geometries on classical and quantum statesen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
from_ENTROPY_2020.pdf
Size:
482.92 KB
Format:
Adobe Portable Document Format