Entanglement Swapping Through The Amplitude Damping Noise Channel

Entanglement Swapping Through The Amplitude Damping Noise Channel | 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Entanglement Swapping Through The Amplitude Damping Noise Channel Jianbo Xing, Fan Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7760185/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract This paper investigates the degradation mechanism of the photon-number-encoded entanglement swapping protocol under the amplitude damping noise channel. By establishing a beam splitter physical model to simulate the energy dissipation process, the evolution density matrix of the input states |ψ⟩ AB = α |00⟩ + β |11⟩ and |ψ⟩ CD = m |00⟩ + n |11⟩ under independent noise channels is analytically derived, and the density matrix, fidelity, and concurrence of the target particle pair after entan-glement swapping are presented. Furthermore, for the case where the initial states are maximally entangled states, this paper numerically simulates the variation curves of the fidelity and concurrence of the system after entanglement swapping with the noise parameter. The results show that as the noise intensity increases, both the fidelity and concurrence of the target system exhibit a decreasing trend. Simultaneously, due to the presence of noise, even if the input states are maximally entangled, the entanglement of the target system after swapping may be destroyed. Based on this, the study further deduces the constraint conditions required to maintain system entanglement in this scenario. Given the restrictive effect of these constraints on entanglement maintenance, this paper also specifically examines the fidelity and concurrence of the target state output from entanglement swapping in the case of 50 : 50 beam splitters when the input states are both maximally entangled. The research finds that in this case, since the constraints are not satisfied, even if the input states are maximally entangled, the entanglement of the output state completely disappears. Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 09 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 03 Nov, 2025 Reviews received at journal 29 Oct, 2025 Reviews received at journal 20 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 12 Oct, 2025 Reviewers invited by journal 08 Oct, 2025 Editor invited by journal 08 Oct, 2025 Editor assigned by journal 06 Oct, 2025 Submission checks completed at journal 03 Oct, 2025 First submitted to journal 01 Oct, 2025 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-7760185","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":533025974,"identity":"bc597a15-3a80-4af5-a14c-0e2ffdba4ea6","order_by":0,"name":"Jianbo Xing","email":"","orcid":"","institution":"Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Jianbo","middleName":"","lastName":"Xing","suffix":""},{"id":533025976,"identity":"8753f97c-8c7d-4a10-af54-7dfba3173da4","order_by":1,"name":"Fan Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYBAC9gYGNhAtZwDmshGhhecARJkx6VoSNxCvRbr92YOfO2rTt0v3GDB8KDvMwD+7gYAWmQPphr1njufunHPGgHHGucMMEncO4NdiL5FwTIK37Vjuhhs5Bsy8bYcZDCQSCNgikdgm+bftWLoBSMtf4rQks0nzttUkgLUwEqcljU1atu2A4c4ZaQUHe86l80jcIKgl/Znk27Y6eXOJ5I0PfpRZy/HPIKAFCg6DyQMgM4hSDwR1xCocBaNgFIyCkQgA9ddAwRykkNcAAAAASUVORK5CYII=","orcid":"","institution":"Beijing Normal University","correspondingAuthor":true,"prefix":"","firstName":"Fan","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2025-10-01 14:24:51","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7760185/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7760185/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-39183-2","type":"published","date":"2026-02-09T15:58:29+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":94141988,"identity":"0f076d3d-70cf-4649-83d8-ac11bc515664","added_by":"auto","created_at":"2025-10-22 20:15:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":347689,"visible":true,"origin":"","legend":"","description":"","filename":"EntanglementSwappingThroughTheAmplitudeDampingNoiseChannel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7760185/v1/4652867663f9147f6a8052ac.pdf"},{"id":94141987,"identity":"42abc242-00ed-480b-a97b-c4adc0d9bec2","added_by":"auto","created_at":"2025-10-22 20:15:04","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4352,"visible":true,"origin":"","legend":"","description":"","filename":"b3dce784da4d4093bd4eb49666d74041.json","url":"https://assets-eu.researchsquare.com/files/rs-7760185/v1/a78a753ca9cbd31dc16c12e1.json"},{"id":102785382,"identity":"bb2eb36d-0735-4c84-b3e4-6a3232003a75","added_by":"auto","created_at":"2026-02-16 16:06:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":434366,"visible":true,"origin":"","legend":"","description":"","filename":"EntanglementSwappingThroughTheAmplitudeDampingNoiseChannel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7760185/v1_covered_e4f4146c-3e70-4140-ad38-addf75e163d5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Entanglement Swapping Through The Amplitude Damping Noise Channel","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7760185/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7760185/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper investigates the degradation mechanism of the photon-number-encoded entanglement swapping protocol under the amplitude damping noise channel. By establishing a beam splitter physical model to simulate the energy dissipation process, the evolution density matrix of the input states |ψ⟩ AB = α |00⟩ + β |11⟩ and |ψ⟩ CD = m |00⟩ + n |11⟩ under independent noise channels is analytically derived, and the density matrix, fidelity, and concurrence of the target particle pair after entan-glement swapping are presented. Furthermore, for the case where the initial states are maximally entangled states, this paper numerically simulates the variation curves of the fidelity and concurrence of the system after entanglement swapping with the noise parameter. The results show that as the noise intensity increases, both the fidelity and concurrence of the target system exhibit a decreasing trend. Simultaneously, due to the presence of noise, even if the input states are maximally entangled, the entanglement of the target system after swapping may be destroyed. Based on this, the study further deduces the constraint conditions required to maintain system entanglement in this scenario. Given the restrictive effect of these constraints on entanglement maintenance, this paper also specifically examines the fidelity and concurrence of the target state output from entanglement swapping in the case of 50 : 50 beam splitters when the input states are both maximally entangled. The research finds that in this case, since the constraints are not satisfied, even if the input states are maximally entangled, the entanglement of the output state completely disappears.","manuscriptTitle":"Entanglement Swapping Through The Amplitude Damping Noise Channel","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-22 20:14:59","doi":"10.21203/rs.3.rs-7760185/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-03T10:55:18+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-29T18:10:20+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-21T01:36:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"305213522896969781538201690311343200550","date":"2025-10-14T17:56:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"21707686144018988237412595482597539462","date":"2025-10-12T09:23:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-08T17:23:17+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-08T17:06:09+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-06T17:33:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-04T01:19:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-10-01T14:00:47+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bf9b1eab-bae2-4158-9d65-bf2c0bca7102","owner":[],"postedDate":"October 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":56666478,"name":"Physical sciences/Mathematics and computing"},{"id":56666479,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-02-16T16:02:57+00:00","versionOfRecord":{"articleIdentity":"rs-7760185","link":"https://doi.org/10.1038/s41598-026-39183-2","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-02-09 15:58:29","publishedOnDateReadable":"February 9th, 2026"},"versionCreatedAt":"2025-10-22 20:14:59","video":"","vorDoi":"10.1038/s41598-026-39183-2","vorDoiUrl":"https://doi.org/10.1038/s41598-026-39183-2","workflowStages":[]},"version":"v1","identity":"rs-7760185","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7760185","identity":"rs-7760185","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}