Entanglement-enhanced quantum lock-in detection achieving simultaneous Heisenberg scalings with particle number and time

Entanglement-enhanced quantum lock-in detection achieving simultaneous Heisenberg scalings with particle number and time | 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 Entanglement-enhanced quantum lock-in detection achieving simultaneous Heisenberg scalings with particle number and time Jiawei Zhang, Min Zhuang, Bing Wang, Yuan Wenfei, Li Jiachong, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6368311/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Dec, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Quantum lock-in detection (QLID), a cornerstone technique in quantum metrology, enables precise extraction of oscillating signals from noise by leveraging dynamical decoupling to suppress unwanted spectral components. Beyond this, many-body quantum entanglement serves as a critical resource for surpassing the standard quantum limit in precision measurements. Here we report the first experimental realization of entanglement-enhanced QLID using two (^{40}\text{Ca}^+) ions confined in a linear Paul trap. The system is initialized into a maximally entangled Greenberger-Horne-Zeilinger state via a M$\phi$lmer-S$\phi$rensen gate, followed by the application of periodic multipulse sequences to implement QLID. Compared to non-entangled states (e.g., a product state), our work demonstrates frequency measurement precision scaling as $1/N$ with particle number (N) , achieving the Heisenberg scaling. Remarkably, the precision in the time domain approaches a super-Heisenberg scaling (i.e., $1/T^2$), significantly outperforming conventional bounds. To enhance practical applicability, we further optimize multipulse sequences to improve robustness against rotation angle inaccuracies and detuning errors. This work establishes QLID as a powerful paradigm for quantum sensing and provides a concrete pathway to Heisenberg-limited detection of oscillating signals in realistic settings. Physical sciences/Physics/Quantum physics/Quantum metrology Physical sciences/Physics/Quantum physics/Qubits Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Published Journal Publication published 06 Dec, 2025 Read the published version in Nature Communications → 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-6368311","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":451113409,"identity":"cec1871f-a549-4cfd-aa32-6559f4e761dd","order_by":0,"name":"Jiawei 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