General theory of measurement with two copies of a quantum state

Autores
Bendersky, Ariel Martin; Paz, Juan Pablo; Cunha, Marcelo Terra
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that μ can label a set of outcomes of a measurement on two copies if and only if there is a family of maps Cμ such that the probability Prob(μ) is the fidelity of each map, i.e., Prob(μ)=Tr[ρCμ(ρ)]. Here, the map Cμ must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure). © 2009 The American Physical Society.
Fil: Bendersky, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Paz, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Cunha, Marcelo Terra. Departamento de Matemática; Brasil
Materia
Quantum Information
Quantum Foundations
Quantum Algorithms
Quantum Measurement
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/61403
Acceder
id CONICETDig_75e32ca4f3d87d6cfd7793cbbbd8384a
oai_identifier_str oai:ri.conicet.gov.ar:11336/61403
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling General theory of measurement with two copies of a quantum stateBendersky, Ariel MartinPaz, Juan PabloCunha, Marcelo TerraQuantum InformationQuantum FoundationsQuantum AlgorithmsQuantum Measurementhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that μ can label a set of outcomes of a measurement on two copies if and only if there is a family of maps Cμ such that the probability Prob(μ) is the fidelity of each map, i.e., Prob(μ)=Tr[ρCμ(ρ)]. Here, the map Cμ must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure). © 2009 The American Physical Society.Fil: Bendersky, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Paz, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Cunha, Marcelo Terra. Departamento de Matemática; BrasilAmerican Physical Society2009-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/61403Bendersky, Ariel Martin; Paz, Juan Pablo; Cunha, Marcelo Terra; General theory of measurement with two copies of a quantum state; American Physical Society; Physical Review Letters; 103; 4; 7-2009; 40404-404040031-9007CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.103.040404info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevLett.103.040404info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:01Zoai:ri.conicet.gov.ar:11336/61403instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:48:01.585CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv General theory of measurement with two copies of a quantum state
title General theory of measurement with two copies of a quantum state
spellingShingle General theory of measurement with two copies of a quantum state
Bendersky, Ariel Martin
Quantum Information
Quantum Foundations
Quantum Algorithms
Quantum Measurement
title_short General theory of measurement with two copies of a quantum state
title_full General theory of measurement with two copies of a quantum state
title_fullStr General theory of measurement with two copies of a quantum state
title_full_unstemmed General theory of measurement with two copies of a quantum state
title_sort General theory of measurement with two copies of a quantum state
dc.creator.none.fl_str_mv Bendersky, Ariel Martin
Paz, Juan Pablo
Cunha, Marcelo Terra
author Bendersky, Ariel Martin
author_facet Bendersky, Ariel Martin
Paz, Juan Pablo
Cunha, Marcelo Terra
author_role author
author2 Paz, Juan Pablo
Cunha, Marcelo Terra
author2_role author
author
dc.subject.none.fl_str_mv Quantum Information
Quantum Foundations
Quantum Algorithms
Quantum Measurement
topic Quantum Information
Quantum Foundations
Quantum Algorithms
Quantum Measurement
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that μ can label a set of outcomes of a measurement on two copies if and only if there is a family of maps Cμ such that the probability Prob(μ) is the fidelity of each map, i.e., Prob(μ)=Tr[ρCμ(ρ)]. Here, the map Cμ must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure). © 2009 The American Physical Society.
Fil: Bendersky, Ariel Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Paz, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Cunha, Marcelo Terra. Departamento de Matemática; Brasil
description We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that μ can label a set of outcomes of a measurement on two copies if and only if there is a family of maps Cμ such that the probability Prob(μ) is the fidelity of each map, i.e., Prob(μ)=Tr[ρCμ(ρ)]. Here, the map Cμ must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure). © 2009 The American Physical Society.
publishDate 2009
dc.date.none.fl_str_mv 2009-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/61403
Bendersky, Ariel Martin; Paz, Juan Pablo; Cunha, Marcelo Terra; General theory of measurement with two copies of a quantum state; American Physical Society; Physical Review Letters; 103; 4; 7-2009; 40404-40404
0031-9007
CONICET Digital
CONICET
url http://hdl.handle.net/11336/61403
identifier_str_mv Bendersky, Ariel Martin; Paz, Juan Pablo; Cunha, Marcelo Terra; General theory of measurement with two copies of a quantum state; American Physical Society; Physical Review Letters; 103; 4; 7-2009; 40404-40404
0031-9007
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.103.040404
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevLett.103.040404
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842268897444626432
score 13.13397

Publicaciones similares