On the curvature of the quantum state space with pull-back metrics
| dc.creator | Andai, Attila | |
| dc.date | 2006-04-14 | |
| dc.date.accessioned | 2026-07-07T08:55:53Z | |
| dc.date.available | 2026-07-07T08:55:53Z | |
| dc.description | The aim of the paper is to extend the notion of $α$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these Riemannian manifolds. We introduce a more general class of pull-back metrics of the noncommutative state spaces, we pull back the Euclidean Riemannian metric of the space of self-adjoint matrices with functions which have an analytic extension to a neighborhood of the interval $]0,1[$ and whose derivative are nowhere zero. We compute the scalar curvature in this setting, and as a corollary we have the scalar curvature of the classical probability space when it is endowed with such a general pull-back metric. In the noncommutative setting we consider real and complex state spaces too. We give a simplification of Gibilisco's and Isola's conjecture for the first nontrivial classical probability space and we present the result of a numerical computation which indicate that the conjecture may be true for the space of real and complex qubits. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0604031 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0604031 | |
| dc.identifier | Linear Algebra and Its Applications, 423, 287-304, 2007. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146420 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 53C20; 81Q99 | |
| dc.title | On the curvature of the quantum state space with pull-back metrics | |
| dc.type | text |