Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems

Abstract Hilbert–Schmidt speed (HSS) is a special type of quantum statistical speed which is easily computable, since it does not require diagonalization of the system state. We find that, when both HSS and quantum Fisher information (QFI) are calculated with respect to the phase parameter encoded i...

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Autores principales:	Hossein Rangani Jahromi, Rosario Lo Franco
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/2630e41bbd2241ad9224c95df0938d7d
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spelling	oai:doaj.org-article:2630e41bbd2241ad9224c95df0938d7d2021-12-02T13:27:08ZHilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems10.1038/s41598-021-86461-22045-2322https://doaj.org/article/2630e41bbd2241ad9224c95df0938d7d2021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-86461-2https://doaj.org/toc/2045-2322Abstract Hilbert–Schmidt speed (HSS) is a special type of quantum statistical speed which is easily computable, since it does not require diagonalization of the system state. We find that, when both HSS and quantum Fisher information (QFI) are calculated with respect to the phase parameter encoded into the initial state of an n-qubit register, the zeros of the HSS dynamics are actually equal to those of the QFI dynamics. Moreover, the signs of the time-derivatives of both HSS and QFI exactly coincide. These findings, obtained via a thorough investigation of several paradigmatic open quantum systems, show that HSS and QFI exhibit the same qualitative time evolution. Therefore, HSS reveals itself as a powerful figure of merit for enhancing quantum phase estimation in an open quantum system made of n qubits. Our results also provide strong evidence for both contractivity of the HSS under memoryless dynamics and its sensitivity to system-environment information backflows to detect the non-Markovianity in high-dimensional systems, as suggested in previous studies.Hossein Rangani JahromiRosario Lo FrancoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-16 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Hossein Rangani Jahromi Rosario Lo Franco Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems
description	Abstract Hilbert–Schmidt speed (HSS) is a special type of quantum statistical speed which is easily computable, since it does not require diagonalization of the system state. We find that, when both HSS and quantum Fisher information (QFI) are calculated with respect to the phase parameter encoded into the initial state of an n-qubit register, the zeros of the HSS dynamics are actually equal to those of the QFI dynamics. Moreover, the signs of the time-derivatives of both HSS and QFI exactly coincide. These findings, obtained via a thorough investigation of several paradigmatic open quantum systems, show that HSS and QFI exhibit the same qualitative time evolution. Therefore, HSS reveals itself as a powerful figure of merit for enhancing quantum phase estimation in an open quantum system made of n qubits. Our results also provide strong evidence for both contractivity of the HSS under memoryless dynamics and its sensitivity to system-environment information backflows to detect the non-Markovianity in high-dimensional systems, as suggested in previous studies.
format	article
author	Hossein Rangani Jahromi Rosario Lo Franco
author_facet	Hossein Rangani Jahromi Rosario Lo Franco
author_sort	Hossein Rangani Jahromi
title	Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems
title_short	Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems
title_full	Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems
title_fullStr	Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems
title_full_unstemmed	Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems
title_sort	hilbert–schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/2630e41bbd2241ad9224c95df0938d7d
work_keys_str_mv	AT hosseinranganijahromi hilbertschmidtspeedasanefficientfigureofmeritforquantumestimationofphaseencodedintotheinitialstateofopennqubitsystems AT rosariolofranco hilbertschmidtspeedasanefficientfigureofmeritforquantumestimationofphaseencodedintotheinitialstateofopennqubitsystems
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Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems

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