Navigating the Quantum Resource Landscape of Entropy Vector Space Using Machine Learning and Optimization

Navigating the Quantum Resource Landscape of Entropy Vector Space Using Machine Learning and Optimization | 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 Navigating the Quantum Resource Landscape of Entropy Vector Space Using Machine Learning and Optimization William Munizzi, Aman Mehta, Nothando Khumalo, Prineha Narang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8971516/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, with a focus on violations of entropy inequalities. In particular, we investigate Ingleton’s inequality, which is satisfied by all stabilizer and holographic quantum states. We first prove that violation is impossible for pure states of five qubits or fewer, establishing six qubits as the minimal system size required to cross the Ingleton boundary. Using a reinforcement learning agent formulated as a Markov decision process, we identify quantum circuits that navigate entropy vector space to generate Ingleton-violating states. Complementing this approach with classical optimization, we construct large families of violating states with tunable degrees of violation and empirically determine the maximal attainable violation. Our analysis reveals a sharp resource transition: violation requires substantial total quantum magic but only modest non-local magic, and occurs in statistically rare, sharply-defined regions of Hilbert space. Together, these results establish a unified computational toolkit for probing entropy cone boundaries, tracking quantum resource evolution, and engineering circuits with controlled information-theoretic features. Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files IngletonSupplemental.pdf Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 29 Mar, 2026 Editor assigned by journal 06 Mar, 2026 Submission checks completed at journal 06 Mar, 2026 First submitted to journal 25 Feb, 2026 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-8971516","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":615736080,"identity":"b7762057-668a-4d9f-9c83-5558b3b0eeb0","order_by":0,"name":"William Munizzi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIie3PIQvCQBTA8SeDZ3lqvUPZvsIDYWJxX+VgYLpgEkHQaJld8EuYlgWDZVkGKxPBZJYFgyfalDmb4f7lOLgf7x2AzfavKQBC77QFGL2ulUgThubgquSRC5qrET4kfp7fZh2E5CoKHkCrrrmcZLrHipCwtoxlxCHI6FJO/Ez7QgkidBpxG9gBTr9MeRIWhEhnQ+YQVCOKzWqEhuyAxRcSZMOxUFvzG4HdfsR7Esl5VErkOoxlcZsF3so5psVk6rYW4aaUvEW/PbfZbDbbx+7lkzi/+FHBzwAAAABJRU5ErkJggg==","orcid":"","institution":"University of California, Los Angeles","correspondingAuthor":true,"prefix":"","firstName":"William","middleName":"","lastName":"Munizzi","suffix":""},{"id":615736081,"identity":"33648249-7e5f-4fdd-9ba1-e7064cba4fe9","order_by":1,"name":"Aman Mehta","email":"","orcid":"","institution":"University of California, Los Angeles","correspondingAuthor":false,"prefix":"","firstName":"Aman","middleName":"","lastName":"Mehta","suffix":""},{"id":615736082,"identity":"855cc4a2-bc51-40bf-9a22-2669f8ea4896","order_by":2,"name":"Nothando Khumalo","email":"","orcid":"","institution":"University of California, Los Angeles","correspondingAuthor":false,"prefix":"","firstName":"Nothando","middleName":"","lastName":"Khumalo","suffix":""},{"id":615736083,"identity":"9525927b-9c6e-4241-8a8d-0ce7066ba465","order_by":3,"name":"Prineha Narang","email":"","orcid":"","institution":"University of California, Los Angeles","correspondingAuthor":false,"prefix":"","firstName":"Prineha","middleName":"","lastName":"Narang","suffix":""}],"badges":[],"createdAt":"2026-02-25 22:23:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8971516/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8971516/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106094361,"identity":"386b93a7-dde9-4ce7-bcd0-3cb91740ce9c","added_by":"auto","created_at":"2026-04-03 11:42:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1410042,"visible":true,"origin":"","legend":"","description":"","filename":"npjSubmissionUpdated.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8971516/v1_covered_04966ad2-6493-42cb-8a39-9d5c58756e02.pdf"},{"id":106053748,"identity":"24a9d370-370c-4514-88ba-7a0ccd40c5f1","added_by":"auto","created_at":"2026-04-03 00:22:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":369491,"visible":true,"origin":"","legend":"","description":"","filename":"IngletonSupplemental.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8971516/v1/97af9f0f5ccdff2d43bbc4be.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Navigating the Quantum Resource Landscape of Entropy Vector Space Using Machine Learning and Optimization","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"npj-quantum-information","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjqi","sideBox":"Learn more about [npj Quantum Information](http://www.nature.com/npjqi/)","snPcode":"41534","submissionUrl":"https://mts-npjqi.nature.com/","title":"npj Quantum Information","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8971516/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8971516/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, with a focus on violations of entropy inequalities. 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