On the Curvature of Monotone Metrics and a Conjecture Concerning the Kubo-Mori Metric

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dc.creatorDittmann, J.
dc.date1999-06-02
dc.date.accessioned2026-07-07T06:16:37Z
dc.date.available2026-07-07T06:16:37Z
dc.descriptionIt is the aim of this article to determine curvature quantities of an arbitrary Riemannian monotone metric on the space of positive matrices resp. nonsingular density matrices. Special interest is focused on the scalar curvature due to its expected quantum statistical meaning. The scalar curvature is explained in more detail for three examples, the Bures metric, the largest monotone metric and the Kubo-Mori metric. In particular, we show an important conjecture of Petz concerning the Kubo-Mori metric up to a formal proof of the concavity of a certain function on R_+^3. This concavity seems to be numerically evident. The conjecture of Petz asserts that the scalar curvature of the Kubo-Mori metric increases if one goes to more mixed states.
dc.description20 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/9906009
dc.identifierhttp://arxiv.org/abs/quant-ph/9906009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94116
dc.subjectQuantum Physics
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.titleOn the Curvature of Monotone Metrics and a Conjecture Concerning the Kubo-Mori Metric
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