General theory of measurement with two copies of a quantum state

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 outco...

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Detalles Bibliográficos
Autores principales:	Bendersky, Ariel Martín, Paz, Juan Pablo
Publicado:	2009
Materias:	Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00319007_v103_n4_p_Bendersky http://hdl.handle.net/20.500.12110/paper_00319007_v103_n4_p_Bendersky
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00319007_v103_n4_p_Bendersky
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spelling	paper:paper_00319007_v103_n4_p_Bendersky2023-06-08T14:57:51Z General theory of measurement with two copies of a quantum state Bendersky, Ariel Martín Paz, Juan Pablo Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory 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, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paz, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00319007_v103_n4_p_Bendersky http://hdl.handle.net/20.500.12110/paper_00319007_v103_n4_p_Bendersky
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory
spellingShingle	Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory Bendersky, Ariel Martín Paz, Juan Pablo General theory of measurement with two copies of a quantum state
topic_facet	Completely positive Copositive General theory Positive operator valued measure Quantum state Quantum state tomography Labels Tomography Quantum theory
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.
author	Bendersky, Ariel Martín Paz, Juan Pablo
author_facet	Bendersky, Ariel Martín Paz, Juan Pablo
author_sort	Bendersky, Ariel Martín
title	General theory of measurement with two copies of a quantum state
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
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00319007_v103_n4_p_Bendersky http://hdl.handle.net/20.500.12110/paper_00319007_v103_n4_p_Bendersky
work_keys_str_mv	AT benderskyarielmartin generaltheoryofmeasurementwithtwocopiesofaquantumstate AT pazjuanpablo generaltheoryofmeasurementwithtwocopiesofaquantumstate
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General theory of measurement with two copies of a quantum state

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