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Semigrupos cuánticos de Markov: pasado, presente y futuro

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dc.contributor.authorAgredo Echeverry, Julián Andrésspa
dc.date.accessioned2017-07-16 00:00:00
dc.date.accessioned2022-06-13T17:42:07Z
dc.date.available2017-07-16 00:00:00
dc.date.available2022-06-13T17:42:07Z
dc.date.issued2017-07-16
dc.description.abstractLos semigrupos cuánticos de Markov (SCM) son una extensión no conmutativa de los semigrupos de Markov definidos en probabilidad clásica. Ellos representan una evolución sin memoria de un sistema microscopico acorde a las leyes de la física cuántica y a la estructura de los sistemas cuánticos abiertos. Esto significa que la dinámica reducida del sistema principal es descrita por un espacio de Hilbert separable complejo ???? por medio de un semigrupo ????=(????t)t≥0, el cual actúa sobre una subálgebra de von Neumann ???? del álgebra ????(????) de todos los operadores lineales acotados definidos en ????. Por simplicidad, algunas veces asumiremos que ????=????(????). El semigrupo ???? corresponde al cuadro de Heisenberg en el sentido que dado cualquier observable x, ????t(x) describe su evolución en el tiempo t. De esta forma, dada una matriz de densidad p, su dinámica (cuadro de Schrödinger) es dada por el semigrupo predual ????*t(ρ) , donde tr(ρ????t(x))=tr(????*t(ρ)x), tr(⋅) denota la operación traza. En este trabajo ofrecemos una exposición de varios resultados básicos sobre SCM. Además discutimos aplicaciones de SCM en teoría de la información cuántica y computación cuántica.spa
dc.description.abstractQuantum Markov semigroups (SCM) are a non-commutative extension of the Markov semigroups defined in classical probability. They represent an evolution without memory of a microscopic system according to the laws of quantum physics and the structure of open quantum systems. This means that the reduced dynamics of the main system is described by a complex separable Hilbert space ???? by means of a semigroup ????=(????t)t≥0, acting on a von Neumann algebra ????(????) of the linear operators defined on ????. For simplicity, we will sometimes assume that ????=????(????). The semigroup ???? corresponds to the Heisenberg picture in the sense that given any observable x, ????t(x) describes its evolution at time t. Thus, given a density matrix p, its dynamics (Schrödinger's picure) is given by the predual semigroup ????*t(ρ), where tr(ρ????t(x))=tr(????*t(ρ)x), tr(⋅) denote trace of a matrix. In this paper we offer an exposition of several basic results on SCM. We also discuss SCM applications in quantum information theory and quantum computing.eng
dc.format.mimetypeapplication/pdfspa
dc.identifier.doi10.22579/20112629.427
dc.identifier.eissn2011-2629
dc.identifier.issn0121-3709
dc.identifier.urihttps://repositorio.unillanos.edu.co/handle/001/2649
dc.identifier.urlhttps://doi.org/10.22579/20112629.427
dc.language.isospaspa
dc.publisherUniversidad de los Llanosspa
dc.relation.bitstreamhttps://orinoquia.unillanos.edu.co/index.php/orinoquia/article/download/427/1018
dc.relation.citationeditionNúm. 1 Sup , Año 2017spa
dc.relation.citationendpage29
dc.relation.citationissue1 Supspa
dc.relation.citationstartpage20
dc.relation.citationvolume21spa
dc.relation.ispartofjournalOrinoquiaspa
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dc.rightsOrinoquia - 2019spa
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dc.rights.urihttps://creativecommons.org/licenses/by/4.0/spa
dc.sourcehttps://orinoquia.unillanos.edu.co/index.php/orinoquia/article/view/427spa
dc.subjectEditorialeng
dc.subjectEditorialspa
dc.titleSemigrupos cuánticos de Markov: pasado, presente y futurospa
dc.title.translatedQuantum Markov semigroups (QMS): past, present and future panoramaeng
dc.typeArtículo de revistaspa
dc.typeJournal Articleeng
dc.type.coarhttp://purl.org/coar/resource_type/c_6501spa
dc.type.coarversionhttp://purl.org/coar/version/c_970fb48d4fbd8a85spa
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dc.type.driverinfo:eu-repo/semantics/articlespa
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