Imaginarity-free quantum multiparameter estimation

Multiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated until you discover the optimal measurement. Third, the optimal m...

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Main Authors: Jisho Miyazaki, Keiji Matsumoto
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2022-03-01
Series:Quantum
Online Access:https://quantum-journal.org/papers/q-2022-03-10-665/pdf/
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author Jisho Miyazaki
Keiji Matsumoto
author_facet Jisho Miyazaki
Keiji Matsumoto
author_sort Jisho Miyazaki
collection DOAJ
description Multiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated until you discover the optimal measurement. Third, the optimal measurement may generally depend on the target values of parameters, and thus may be impossible to perform for unknown target states. We present a method to circumvent these three obstacles. A class of quantum statistical models, which utilizes antiunitary symmetries or, equivalently, real density matrices, offers compatible multiparameter estimations. The symmetries accompany the target-independent optimal measurements for pure-state models. Based on this finding, we propose methods to implement antiunitary symmetries for quantum metrology schemes. We further introduce a function which measures antiunitary asymmetry of quantum statistical models as a potential tool to characterize quantumness of phase transitions.
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spelling doaj.art-983235b020f046dcb97ea21492226edb2022-12-21T23:52:45ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2022-03-01666510.22331/q-2022-03-10-66510.22331/q-2022-03-10-665Imaginarity-free quantum multiparameter estimationJisho MiyazakiKeiji MatsumotoMultiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated until you discover the optimal measurement. Third, the optimal measurement may generally depend on the target values of parameters, and thus may be impossible to perform for unknown target states. We present a method to circumvent these three obstacles. A class of quantum statistical models, which utilizes antiunitary symmetries or, equivalently, real density matrices, offers compatible multiparameter estimations. The symmetries accompany the target-independent optimal measurements for pure-state models. Based on this finding, we propose methods to implement antiunitary symmetries for quantum metrology schemes. We further introduce a function which measures antiunitary asymmetry of quantum statistical models as a potential tool to characterize quantumness of phase transitions.https://quantum-journal.org/papers/q-2022-03-10-665/pdf/
spellingShingle Jisho Miyazaki
Keiji Matsumoto
Imaginarity-free quantum multiparameter estimation
Quantum
title Imaginarity-free quantum multiparameter estimation
title_full Imaginarity-free quantum multiparameter estimation
title_fullStr Imaginarity-free quantum multiparameter estimation
title_full_unstemmed Imaginarity-free quantum multiparameter estimation
title_short Imaginarity-free quantum multiparameter estimation
title_sort imaginarity free quantum multiparameter estimation
url https://quantum-journal.org/papers/q-2022-03-10-665/pdf/
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AT keijimatsumoto imaginarityfreequantummultiparameterestimation