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Quantum Markov semigroups (QMS): past, present and future panorama Semigrupos quánticos de Markov: Pasado, pressente e futuro

dc.contributor.authorAgredo Echeverry, Julián Andrés
dc.date.accessioned2021-05-05T22:53:27Z
dc.date.accessioned2021-10-01T17:20:45Z
dc.date.available2021-05-05
dc.date.available2021-10-01T17:20:45Z
dc.date.issued2017
dc.identifier.issn2011-2629
dc.identifier.urihttps://repositorio.escuelaing.edu.co/handle/001/1396
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 h por medio de un semigrupo T=(Tt)t≥0, el cual actúa sobre una subálgebra de von Neumann M del álgebra P(h) de todos los operadores lineales acotados definidos en h. Por simplicidad, algunas veces asumiremos que M=P(h). El semigrupo T corresponde al cuadro de Heisenberg en el sentido que dado cualquier observable x, Tt(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*t(ρ) , donde tr(ρTt(x))=tr(T*t(ρ)x), tr(⋅) denota p, su dinámica (cuadro de Schrödinger) es dada por el semigrupo predual T*t(ρ) , donde tr(ρTt(x))=tr(T*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 (QMS) are a non-commutative extension of Markov semigroups defined in classical probability. They represent a memoryless evolution 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 h by means of a semigroup T=(Tt)t≥0, which acts on a von Neumann subalgebra M of the algebra P(h) of all bounded linear operators defined on h. For simplicity, we will sometimes assume that M=P(h). The semigroup T corresponds to the Heisenberg picture in the sense that given any observable x, Tt(x) describes its evolution in time t. Thus, given a density matrix p, its dynamics (Schrödinger square) is given by the predual semigroup T*t(ρ) , where tr(ρTt(x))=tr(T*t(ρ)x), tr(⋅) denotes p, its dynamics (Schrödinger frame) is given by the predual semigroup T*t(ρ) , where tr(ρTt(x))=tr(T*t(ρ)x), tr(⋅) denotes the trace operation. In this paper we provide an exposition of several basic results on SCM. In addition, we discuss applications of SCM in quantum information theory and quantum computation.spa
dc.format.extent10 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.language.isospaspa
dc.publisherUniversidad de los Llanosspa
dc.sourcehttps://orinoquia.unillanos.edu.co/index.php/orinoquia/article/view/427spa
dc.titleSemigrupos cuánticos de Markov: Pasado, presente y futurospa
dc.titleQuantum Markov semigroups (QMS): past, present and future panorama Semigrupos quánticos de Markov: Pasado, pressente e futuroeng
dc.typeArtículo de revistaspa
dc.description.notes1 Matemático, MSc, Phd. Grupo de investigación GIMATH, Escuela Colombiana de Ingeniería Julio Garavito, Bogotá, Colombia Email: julian.agredo@escuelaing.edu.cospa
dc.type.versioninfo:eu-repo/semantics/publishedVersionspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa
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dc.contributor.researchgroupMatemáticasspa
dc.identifier.doi10.22579/20112629.427
dc.identifier.urlhttps://doi.org/10.22579/20112629.427
dc.publisher.placeColombia, Orinoquiaspa
dc.relation.citationeditionOrinoquia, Volumen 21, Número 1 Sup, p. 20-29, 2017. ISSN electrónico 2011-2629. ISSN impreso 0121-3709.spa
dc.relation.citationendpage29spa
dc.relation.citationissue1spa
dc.relation.citationstartpage20spa
dc.relation.citationvolume21spa
dc.relation.indexedN/Aspa
dc.relation.ispartofjournalRevista Orinoquiaspa
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.subject.armarcTeoria de la información
dc.subject.armarcComputación cuántica
dc.subject.proposalComputación cuánticaspa
dc.subject.proposalSemigrupos de Markov cuánticosspa
dc.subject.proposalTeoria de la informaciónspa
dc.subject.proposalQuantum computingspa
dc.subject.proposalQuantum Markov semigroupsspa
dc.subject.proposalInformation theoryspa
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dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/articlespa
dc.type.redcolhttp://purl.org/redcol/resource_type/ARTspa


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