Tight Bounds on the Simultaneous Estimation of Incompatible Parameters

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables greatly diminishes the applicability of estimation theory in many prac...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Jasminder S. Sidhu, Yingkai Ouyang, Earl T. Campbell, Pieter Kok
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/0f365f6992504cff8ea8c515b8f7ac79
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:0f365f6992504cff8ea8c515b8f7ac79
record_format	dspace
spelling	oai:doaj.org-article:0f365f6992504cff8ea8c515b8f7ac792021-12-02T14:23:21ZTight Bounds on the Simultaneous Estimation of Incompatible Parameters10.1103/PhysRevX.11.0110282160-3308https://doaj.org/article/0f365f6992504cff8ea8c515b8f7ac792021-02-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.011028http://doi.org/10.1103/PhysRevX.11.011028https://doaj.org/toc/2160-3308The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables greatly diminishes the applicability of estimation theory in many practical implementations. The Holevo Cramér-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multiparameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimization over multiple variables. In this work, we develop an analytic approach to solving the HCRB for two parameters. Our analysis reveals the role of the HCRB and its interplay with alternative bounds in estimation theory. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations that even numerically permits a quadratic speedup over previous state-of-the-art approaches. We apply our results to compare the performance of different probe states in magnetic field sensing and characterize the performance of state tomography on the code space of noisy bosonic error-correcting codes. The sensitivity of state tomography on noisy binomial code states can be improved by tuning two coding parameters that relate to the number of correctable phase and amplitude damping errors. Our work provides fundamental insights and makes significant progress toward the estimation of multiple incompatible observables.Jasminder S. SidhuYingkai OuyangEarl T. CampbellPieter KokAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 1, p 011028 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Jasminder S. Sidhu Yingkai Ouyang Earl T. Campbell Pieter Kok Tight Bounds on the Simultaneous Estimation of Incompatible Parameters
description	The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables greatly diminishes the applicability of estimation theory in many practical implementations. The Holevo Cramér-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multiparameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimization over multiple variables. In this work, we develop an analytic approach to solving the HCRB for two parameters. Our analysis reveals the role of the HCRB and its interplay with alternative bounds in estimation theory. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations that even numerically permits a quadratic speedup over previous state-of-the-art approaches. We apply our results to compare the performance of different probe states in magnetic field sensing and characterize the performance of state tomography on the code space of noisy bosonic error-correcting codes. The sensitivity of state tomography on noisy binomial code states can be improved by tuning two coding parameters that relate to the number of correctable phase and amplitude damping errors. Our work provides fundamental insights and makes significant progress toward the estimation of multiple incompatible observables.
format	article
author	Jasminder S. Sidhu Yingkai Ouyang Earl T. Campbell Pieter Kok
author_facet	Jasminder S. Sidhu Yingkai Ouyang Earl T. Campbell Pieter Kok
author_sort	Jasminder S. Sidhu
title	Tight Bounds on the Simultaneous Estimation of Incompatible Parameters
title_short	Tight Bounds on the Simultaneous Estimation of Incompatible Parameters
title_full	Tight Bounds on the Simultaneous Estimation of Incompatible Parameters
title_fullStr	Tight Bounds on the Simultaneous Estimation of Incompatible Parameters
title_full_unstemmed	Tight Bounds on the Simultaneous Estimation of Incompatible Parameters
title_sort	tight bounds on the simultaneous estimation of incompatible parameters
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/0f365f6992504cff8ea8c515b8f7ac79
work_keys_str_mv	AT jasminderssidhu tightboundsonthesimultaneousestimationofincompatibleparameters AT yingkaiouyang tightboundsonthesimultaneousestimationofincompatibleparameters AT earltcampbell tightboundsonthesimultaneousestimationofincompatibleparameters AT pieterkok tightboundsonthesimultaneousestimationofincompatibleparameters
_version_	1718391409810079744

Tight Bounds on the Simultaneous Estimation of Incompatible Parameters

Ejemplares similares