Relationship between average correlation and geometric measure of quantum discord for a class of two-qubit X-states

Relationship between average correlation and geometric measure of quantum discord for a class of two-qubit X-states | 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 Relationship between average correlation and geometric measure of quantum discord for a class of two-qubit X-states Youneng Guo, Xiaojing Ma, Huping Peng, Zhiguang Tan, Qinglong Tian This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6258675/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 Nonclassical correlation is widely regarded as a powerful resource offering quantum advantages in modern quantum-information processing. Various measurements of nonclassicality as well as the relations among them have recently received much attention. Motivated by works on the relations of Bell nonlocality to average correlation(one kind of nonlocal correlations) and to geometric measure of quantum discord, an interesting question arises whether one can establish directly the link of average correlation to geometric measure of quantum discord. In this paper, we address this question by concerning the link of average correlation to a fixed geometric measure of quantum discord for a specific class of two-qubit X-states. In particular, exact lower and upper bounds of average correlation versus geometric discord are derived and the respective states which have extremal bounds are also characterized. Furthermore, the their dynamical behaviors suffered from decoherence are also carefully analyzed. The results show that average correlation is closely related to geometric discord, like its relationship with Bell nonlocality. Physical sciences/Physics/Information theory and computation Physical sciences/Physics Physical sciences/Physics/Quantum physics/Quantum information 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6258675","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":436224028,"identity":"f40b2ec0-892c-43b8-8579-08337997fa58","order_by":0,"name":"Youneng Guo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYDADfmbG9h8fDGzsiNci2d58QHJGQVoy8VoMzhxLkOb5cIixgZBK+YjkY9K8bXZ5DDdyDIxtDA4wM7AfProBnxbDG2nJxrxtycWMM3IMknMM7vAx8KSl3cCrZUaO4WPeNubEZokcg8M5Bs+YGSR4zAhpMTjM21af2CaRY9hsYXCYsYGQFnkJsC2HE3t4jiUzMxCjxYDnWbLhnHPHE2ewNx9j7DFIS2Yj5Bf59uRjEm/KqhP3H2ZsY/jxx8aOn/3wMfy2HAASjGxIImw4VCJsaQCRfwgpGwWjYBSMghENAAYjStguh+ciAAAAAElFTkSuQmCC","orcid":"","institution":"Changsha University","correspondingAuthor":true,"prefix":"","firstName":"Youneng","middleName":"","lastName":"Guo","suffix":""},{"id":436224029,"identity":"c52dd86b-ccea-4cce-b45c-68fc3dddf4ed","order_by":1,"name":"Xiaojing Ma","email":"","orcid":"","institution":"China Satellite Network System CO.,LTD","correspondingAuthor":false,"prefix":"","firstName":"Xiaojing","middleName":"","lastName":"Ma","suffix":""},{"id":436224033,"identity":"17ede1e3-279c-4814-9aaa-71ccb098ae58","order_by":2,"name":"Huping Peng","email":"","orcid":"","institution":"Changsha University","correspondingAuthor":false,"prefix":"","firstName":"Huping","middleName":"","lastName":"Peng","suffix":""},{"id":436224034,"identity":"bccbceb9-3daf-45c7-a531-a456734c6492","order_by":3,"name":"Zhiguang Tan","email":"","orcid":"","institution":"Changsha University","correspondingAuthor":false,"prefix":"","firstName":"Zhiguang","middleName":"","lastName":"Tan","suffix":""},{"id":436224035,"identity":"7725b023-ae40-416c-9d81-2d1e9d96a719","order_by":4,"name":"Qinglong Tian","email":"","orcid":"","institution":"Changsha University","correspondingAuthor":false,"prefix":"","firstName":"Qinglong","middleName":"","lastName":"Tian","suffix":""}],"badges":[],"createdAt":"2025-03-19 06:53:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6258675/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6258675/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86740691,"identity":"de773dd3-daf8-4557-8cd4-0f3c70e1daee","added_by":"auto","created_at":"2025-07-15 06:47:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":553530,"visible":true,"origin":"","legend":"","description":"","filename":"mian.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6258675/v1_covered_1ae37721-ade7-4de0-9115-8ac1f6ec7793.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Relationship between average correlation and geometric measure of quantum discord for a class of two-qubit X-states","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":"","lastPublishedDoi":"10.21203/rs.3.rs-6258675/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6258675/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Nonclassical correlation is widely regarded as a powerful resource offering quantum advantages in modern quantum-information processing. 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