Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation

Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation Hongzhen Chen, Haidong Yuan, Lingna Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4287852/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Oct, 2024 Read the published version in npj Quantum Information → Version 1 posted 9 You are reading this latest preprint version Abstract How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information science. While existing studies have been mostly focusing on the approximation of two observables with a single measurement, in practice multiple observables are often encountered, for which the errors of the approximations are little understood. Here we provide a framework to study the implementation of an arbitrary finite number of observables with a single measurement. Our methodology yields novel analytical bounds on the errors of these implementations, significantly advancing our understanding of this fundamental problem. Additionally, we introduce a more stringent bound utilizing semi-definite programming that, in the context of two observables, generates an analytical bound tighter than previously known bounds. The derived bounds have direct applications in assessing the trade-off between the precision of estimating multiple parameters in quantum metrology, an area with crucial theoretical and practical implications. To validate the validity of our findings, we conducted experimental verification using a superconducting quantum processor. This experimental validation not only confirms the theoretical results but also effectively bridges the gap between the derived bounds and empirical data obtained from real-world experiments. Our work paves the way for optimizing various tasks in quantum information science that involve multiple noncommutative observables. Physical sciences/Physics/Quantum physics/Quantum information Physical sciences/Physics/Quantum physics/Quantum metrology Physical sciences/Physics/Quantum physics/Quantum mechanics Full Text Additional Declarations (Not answered) Supplementary Files multiobsersupp.pdf supplementary text Cite Share Download PDF Status: Published Journal Publication published 06 Oct, 2024 Read the published version in npj Quantum Information → Version 1 posted Editorial decision: revise 02 Jul, 2024 Review # 2 received at journal 30 Jun, 2024 Reviewer # 2 agreed at journal 28 Jun, 2024 Review # 1 received at journal 31 May, 2024 Reviewer # 1 agreed at journal 19 May, 2024 Reviewers invited by journal 14 May, 2024 Submission checks completed at journal 19 Apr, 2024 Editor assigned by journal 18 Apr, 2024 First submitted to journal 18 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4287852","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":302378882,"identity":"3b9817e0-6ab4-44a9-a31f-9d9f8699e14b","order_by":0,"name":"Hongzhen Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYBACAwYGNiBlA+HxkKAljXQth0nQYs5/+NmDjzvO28vPSGB88LaNQd6ckBbLhmPmhjPP3E5snJHAbDi3jcFwZwMhhx3sYZPmbbudwCyRAGIwJBgcIKTlMA+b9N+2c/ZsEgnsv4nTcgyohbHtAGMP0BZm4rScYTOT7G1LTpzB87BZcs45CcMNBLWcP/xM4mebnb18e/LBD2/KbOQJ2oIEGBuAhATx6kfBKBgFo2AU4AYATWE5tn9Z7fsAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-7578-7248","institution":"Shenzhen University","correspondingAuthor":true,"prefix":"","firstName":"Hongzhen","middleName":"","lastName":"Chen","suffix":""},{"id":302378883,"identity":"823170c9-1a04-4d9e-af8d-fad79a211cea","order_by":1,"name":"Haidong Yuan","email":"","orcid":"","institution":"Chinese University of Hong Kong","correspondingAuthor":false,"prefix":"","firstName":"Haidong","middleName":"","lastName":"Yuan","suffix":""},{"id":302378884,"identity":"61561f52-1758-4f55-ae84-7c18bf680364","order_by":2,"name":"Lingna Wang","email":"","orcid":"","institution":"The Chinese University of Hong Kong","correspondingAuthor":false,"prefix":"","firstName":"Lingna","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2024-04-18 12:45:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4287852/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4287852/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41534-024-00894-x","type":"published","date":"2024-10-06T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":66001980,"identity":"b9583e86-1481-4cdd-a220-2a1a138952d0","added_by":"auto","created_at":"2024-10-06 07:06:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":976159,"visible":true,"origin":"","legend":"","description":"","filename":"multiobsermain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4287852/v1_covered_d0adb181-51d5-4655-abd5-be996a28899f.pdf"},{"id":56750624,"identity":"3a44b551-fe0d-4c1c-ac8a-8cf589551bac","added_by":"auto","created_at":"2024-05-20 03:33:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":823171,"visible":true,"origin":"","legend":"\u003cp\u003esupplementary text\u003c/p\u003e","description":"","filename":"multiobsersupp.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4287852/v1/9fa05be2d5c8602a9aeeb01a.pdf"}],"financialInterests":"(Not answered)","formattedTitle":"Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-quantum-information","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjqi","sideBox":"Learn more about [npj Quantum Information](http://www.nature.com/npjqi/)","snPcode":"41534","submissionUrl":"https://mts-npjqi.nature.com/","title":"npj Quantum Information","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4287852/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4287852/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"How well can multiple incompatible observables be implemented by a single measurement? 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