Operational entanglement of collective quantum modes at room temperature

Operational entanglement of collective quantum modes at room temperature | 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 Operational entanglement of collective quantum modes at room temperature Shalender Singh, Santosh Kumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8460024/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 Quantum entanglement is commonly assumed to be fragile at ambient temperature and over macroscopic distances, where thermal noise and dissipation are expected to rapidly suppress nonclassical correlations. Here we show that this intuition fails for collective quantum modes whose dynamics is governed by reduced open-system channels rather than by microscopic thermal equilibrium. For two spatially separated collective modes, we derive an exact entanglement boundary based on the positivity of the partial transpose, valid in the symmetric resonant limit. From this result we obtain an explicit minimum collective fluctuation amplitude, expressed entirely in measurable noise, bandwidth, dissipation, and distance-dependent coupling parameters, required to sustain steady-state entanglement at finite temperature. We further show that large collective occupation suppresses but does not eliminate quantum phase diffusion, so the steady state remains phase symmetric and does not collapse to a classical mean-field despite macroscopic signal amplitudes. Stochastic simulations of the reduced open-system dynamics, together with matched classical correlated-noise null models analyzed through an identical pipeline, confirm that entanglement witnesses are violated only in the quantum regime. Our results establish a minimal, platform-independent framework connecting collective-mode dynamics, noise injection, distance, and operational certification of macroscopic entanglement. Physical sciences/Physics/Quantum physics/Qubits Physical sciences/Physics/Quantum physics/Quantum information Full Text Additional Declarations There is NO Competing Interest. 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. 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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-8460024","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":566115862,"identity":"8d13ec77-c63c-4b82-9de5-1f9b8ffe5f9f","order_by":0,"name":"Shalender Singh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIie3RMUvDQBTA8XdkyHKS9QXFfIVXOjgU6lc5yZAlBMeCYIXCudT9ip/CRRwvHNTlugfqkC8g1C1CBUOL2CU9uxW8/3bH/eAdD8DnO8YQmAYIAMI7ALG54k4CW8L1huABBMXP2UGSx0mtP14G5xez9/mqXg9vo3ChoRk9dxJ6m1M5s1n/bFmkSvAU42kh2NQuuwkKMifSXKnTvA8CA6SKU8BkN0lUtjJf0oxVbFtCY7x0EahyMkwagchbIgwSOghV+XX5ILOe4kUKQr/GyuZU7vtLO9hT/SkHCYYLw5r1TRTd217djPYM9tvOOvRf3oN76T6fz/dv+wbO5VWzx3DEbQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-3677-4043","institution":"Polriqon Inc","correspondingAuthor":true,"prefix":"","firstName":"Shalender","middleName":"","lastName":"Singh","suffix":""},{"id":566115863,"identity":"944dfd8f-ead6-4735-9b50-0d11047f36d5","order_by":1,"name":"Santosh Kumar","email":"","orcid":"","institution":"Polariqon Inc.","correspondingAuthor":false,"prefix":"","firstName":"Santosh","middleName":"","lastName":"Kumar","suffix":""}],"badges":[],"createdAt":"2025-12-27 09:25:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8460024/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8460024/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100358303,"identity":"85e7cffe-d903-4f2a-9120-f6f5cf5cd94e","added_by":"auto","created_at":"2026-01-16 07:20:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":572631,"visible":true,"origin":"","legend":"Article File","description":"","filename":"Operationalentanglementnature.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8460024/v1_covered_9ac2e393-ec46-4860-9a50-1e5dbec139d4.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Operational entanglement of collective quantum modes at room temperature","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-8460024/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8460024/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Quantum entanglement is commonly assumed to be fragile at ambient temperature and over macroscopic distances, where thermal noise and dissipation are expected to rapidly suppress nonclassical correlations. 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