Quantum Semiparametric Estimation

In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here, we propose a theory of quantum semiparametric estimation that can circumvent both challenges and produ...

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Autores principales:	Mankei Tsang, Francesco Albarelli, Animesh Datta
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b3a94c923557494eac2c617204bf8272
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id	oai:doaj.org-article:b3a94c923557494eac2c617204bf8272
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spelling	oai:doaj.org-article:b3a94c923557494eac2c617204bf82722021-12-02T10:59:22ZQuantum Semiparametric Estimation10.1103/PhysRevX.10.0310232160-3308https://doaj.org/article/b3a94c923557494eac2c617204bf82722020-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.031023http://doi.org/10.1103/PhysRevX.10.031023https://doaj.org/toc/2160-3308In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here, we propose a theory of quantum semiparametric estimation that can circumvent both challenges and produce simple analytic bounds for a class of problems in which the dimensions are arbitrarily high, few prior assumptions about the density operator are made, but only a finite number of the unknown parameters are of interest. We also relate our bounds to Holevo’s version of the quantum Cramér-Rao bound, so that they can inherit the asymptotic attainability of the latter in many cases of interest. The theory is especially relevant to the estimation of a parameter that can be expressed as a function of the density operator, such as the expectation value of an observable, the fidelity to a pure state, the purity, or the von Neumann entropy. Potential applications include quantum state characterization for many-body systems, optical imaging, and interferometry, where full tomography of the quantum state is often infeasible and only a few select properties of the system are of interest.Mankei TsangFrancesco AlbarelliAnimesh DattaAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 3, p 031023 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Mankei Tsang Francesco Albarelli Animesh Datta Quantum Semiparametric Estimation
description	In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here, we propose a theory of quantum semiparametric estimation that can circumvent both challenges and produce simple analytic bounds for a class of problems in which the dimensions are arbitrarily high, few prior assumptions about the density operator are made, but only a finite number of the unknown parameters are of interest. We also relate our bounds to Holevo’s version of the quantum Cramér-Rao bound, so that they can inherit the asymptotic attainability of the latter in many cases of interest. The theory is especially relevant to the estimation of a parameter that can be expressed as a function of the density operator, such as the expectation value of an observable, the fidelity to a pure state, the purity, or the von Neumann entropy. Potential applications include quantum state characterization for many-body systems, optical imaging, and interferometry, where full tomography of the quantum state is often infeasible and only a few select properties of the system are of interest.
format	article
author	Mankei Tsang Francesco Albarelli Animesh Datta
author_facet	Mankei Tsang Francesco Albarelli Animesh Datta
author_sort	Mankei Tsang
title	Quantum Semiparametric Estimation
title_short	Quantum Semiparametric Estimation
title_full	Quantum Semiparametric Estimation
title_fullStr	Quantum Semiparametric Estimation
title_full_unstemmed	Quantum Semiparametric Estimation
title_sort	quantum semiparametric estimation
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/b3a94c923557494eac2c617204bf8272
work_keys_str_mv	AT mankeitsang quantumsemiparametricestimation AT francescoalbarelli quantumsemiparametricestimation AT animeshdatta quantumsemiparametricestimation
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Quantum Semiparametric Estimation

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