Empirical Modeling of Entanglement's Metrological Power via Maximized Quantum Fisher Information in Two-Qubit Systems

Empirical Modeling of Entanglement's Metrological Power via Maximized Quantum Fisher Information in Two-Qubit Systems | 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 Empirical Modeling of Entanglement's Metrological Power via Maximized Quantum Fisher Information in Two-Qubit Systems Volkan Erol This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9621779/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI) using extensive numerical analysis of 20,000 randomly generated two-qubit states. Our systematic study reveals strong empirical relationships between the metrological capacity of quantum states and three entanglement measures: concurrence, negativity, and relative entropy of entanglement. Optimization over local unitary transformations produces substantially more predictable relationships than fixed-generator approaches, as confirmed by bootstrap resampling, systematic data binning, and multiple model comparisons. Exponential fits reach R 2 > 0.99 and polynomial models achieve R 2 = 0.999, providing thorough empirical support for saturation behavior in quantum metrological advantage. Even separable states possess robust metrological utility (MQFI/4 ≈ 0.19, p < 0.0001), achieving approximately 19% of maximal Bell-state sensing capacity—confirming the importance of quantum coherence and discord beyond entanglement. Entanglement–metrology relationships remain stable under realistic decoherence, particularly phase damping. Our findings empirically validate predictions from quantum resource theory, establish empirical bounds for quantum sensor optimization, and offer direct practical guidance for the design of quantum sensing protocols. Physical sciences/Mathematics and computing Physical sciences/Physics quantum metrology quantum Fisher information entanglement measures concurrence negativity quantum sensing decoherence Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-9621779","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":640491769,"identity":"4af58c08-4d00-43d9-bc3a-72df0c634e8c","order_by":0,"name":"Volkan Erol","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYFAC5mYYo/EBkOThI6yFsRnOMABpYSNFS5sEiCKoxeB4Y7PBzx0McubtjW2VX3PsZNgYmB8+uoFPy5mDzYm9ZxiMZc4cbLstuy0Z6DA2Y+McPFokZyQ2H+BtY0icIZHYdltyGzNQCw+bNCEtB/+2MdSDtBRLbqsnrIVfIrE5GWhLggRQC+PHbYeJ0MJzsNlYtk3CcAaQIc247TgPGzMBv7CxNx+WfNtmIy/B3nzw489t1fb87M0PH+PTAgXgGGFg5gGThJUjAOMPUlSPglEwCkbBiAEA5ixBVjk/3jQAAAAASUVORK5CYII=","orcid":"","institution":"Marmara University","correspondingAuthor":true,"prefix":"","firstName":"Volkan","middleName":"","lastName":"Erol","suffix":""}],"badges":[],"createdAt":"2026-05-05 18:09:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9621779/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9621779/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109919851,"identity":"0b858ff7-c3ee-4a85-8473-27d9c62a72d1","added_by":"auto","created_at":"2026-05-25 08:56:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1073934,"visible":true,"origin":"","legend":"","description":"","filename":"scirepmqfi.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9621779/v1_covered_ae9b9e6e-3445-45b5-9640-418b9a79624d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Empirical Modeling of Entanglement's Metrological Power via Maximized Quantum Fisher Information in Two-Qubit Systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"quantum metrology, quantum Fisher information, entanglement measures, concurrence, negativity; quantum sensing, decoherence","lastPublishedDoi":"10.21203/rs.3.rs-9621779/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9621779/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI) using extensive numerical analysis of 20,000 randomly generated two-qubit states. Our systematic study reveals strong empirical relationships between the metrological capacity of quantum states and three entanglement measures: concurrence, negativity, and relative entropy of entanglement. Optimization over local unitary transformations produces substantially more predictable relationships than fixed-generator approaches, as confirmed by bootstrap resampling, systematic data binning, and multiple model comparisons. Exponential fits reach R\u003csup\u003e2\u003c/sup\u003e \u0026gt; 0.99 and polynomial models achieve R\u003csup\u003e2\u003c/sup\u003e = 0.999, providing thorough empirical support for saturation behavior in quantum metrological advantage. Even separable states possess robust metrological utility (MQFI/4 ≈ 0.19, p \u0026lt; 0.0001), achieving approximately 19% of maximal Bell-state sensing capacity—confirming the importance of quantum coherence and discord beyond entanglement. Entanglement–metrology relationships remain stable under realistic decoherence, particularly phase damping. Our findings empirically validate predictions from quantum resource theory, establish empirical bounds for quantum sensor optimization, and offer direct practical guidance for the design of quantum sensing protocols.\u003c/p\u003e","manuscriptTitle":"Empirical Modeling of Entanglement's Metrological Power via Maximized Quantum Fisher Information in Two-Qubit Systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-18 05:34:02","doi":"10.21203/rs.3.rs-9621779/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"dc629255-85e1-4324-ae58-a2b6a1d822ce","owner":[],"postedDate":"May 18th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Rejected","date":"2026-05-25T08:48:22+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-24T16:50:18+00:00","index":56,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-23T22:30:52+00:00","index":55,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-16T11:36:59+00:00","index":52,"fulltext":""},{"type":"reviewerAgreed","content":"259462732808673427776221778281752193223","date":"2026-05-16T11:29:51+00:00","index":51,"fulltext":""},{"type":"reviewerAgreed","content":"282850892503385189941065358653812890546","date":"2026-05-16T09:04:19+00:00","index":50,"fulltext":""},{"type":"reviewerAgreed","content":"97385151097438182379932920601412457901","date":"2026-05-14T20:09:44+00:00","index":45,"fulltext":""},{"type":"reviewersInvited","content":"17","date":"2026-05-14T10:35:54+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-05-12T09:36:54+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-07T10:43:40+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-05-07T10:43:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-05-05T17:57:15+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":68155217,"name":"Physical sciences/Mathematics and computing"},{"id":68155218,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-25T08:56:47+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-18 05:34:02","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9621779","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9621779","identity":"rs-9621779","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}