Emergent Causality and Robust Estimation in Open Quantum-Compatible Systems under Non-Unitary Selection

Emergent Causality and Robust Estimation in Open Quantum-Compatible Systems under Non-Unitary Selection | 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 Research Article Emergent Causality and Robust Estimation in Open Quantum-Compatible Systems under Non-Unitary Selection Joonsung Kang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8771353/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 We propose a novel framework for causal inference inspired by the process matrix formalism, where causal structure is not fixed but emerges through the act of observation. Unlike classical Directed Acyclic Graphs (DAGs), our approach treats the measurement process as a source of causal directionality, necessitating a symmetric, observer-aware inference architecture. We reinterpret Missing Not At Random (MNAR) data not as a nuisance, but as a \textit{non-unitary operation} within a causal network, reflecting back-action from the measurement apparatus. By mapping high-dimensional, low-sample-size (HDLSS) challenges to pseudo-density matrix reconstruction, we develop a selection-aware doubly robust estimator. This estimator integrates variational autoencoders (VAE) for latent state tomography and penalized empirical likelihood to achieve sparsity. We demonstrate that the fundamental limits of causal estimation under observer-induced perturbation are mathematically equivalent to decoherence-induced information loss, aligning our framework with the Quantum Cram'er-Rao bound. Quantum Causal Inference Process Matrix Non-Unitary Selection State Tomography Pseudo-Density Matrix Quantum Fisher Information Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryMaterial.ipynb 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-8771353","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":622313722,"identity":"947a56db-4f12-42bb-be4b-47f80af68e0f","order_by":0,"name":"Joonsung Kang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYPCCBCBmbHzw4YcNmHGASC3Mhw1n9qSBtDQQq4UtTZqH7TCYi1eLbnvzsYc/29LkzfnXGEjw8Jy3W9t+GGhLjU00Li1mZ46lG/O25RjunPHGwEDC4nbytjOJQC3H0nIbcGm5kWMmzdhWwbjhxhmDBAOe28lmB4BaGBsO49Ui+bOtwh6k5UAC27lks/MPCWuRADosccP5NqDpbAfszG4QsuXMMWBAnUtL3nCD+TBjY09ygtkNoC0J+PxyvPmY5I+yZNsN5w+2//7zw87e7Hz6wwcfamxwakEAiQQwlQhWmUBQOQjwHwBT9kQpHgWjYBSMghEFANJsa/wuwrrtAAAAAElFTkSuQmCC","orcid":"","institution":"Gangneung-Wonju national university","correspondingAuthor":true,"prefix":"","firstName":"Joonsung","middleName":"","lastName":"Kang","suffix":""}],"badges":[],"createdAt":"2026-02-03 05:41:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8771353/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8771353/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109488238,"identity":"c22617ad-e209-4b82-af48-c84f62ef8e62","added_by":"auto","created_at":"2026-05-18 16:55:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":609985,"visible":true,"origin":"","legend":"","description":"","filename":"quantumbidirectional.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8771353/v1_covered_b43e2777-ff2a-4fba-a8fb-5a3d5406313d.pdf"},{"id":107103774,"identity":"7f557df1-6e92-4090-a459-8951ab7a3502","added_by":"auto","created_at":"2026-04-16 20:05:43","extension":"ipynb","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":48249,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterial.ipynb","url":"https://assets-eu.researchsquare.com/files/rs-8771353/v1/8a7b715ba89958f8df3d1a02.ipynb"}],"financialInterests":"No competing interests reported.","formattedTitle":"Emergent Causality and Robust Estimation in Open Quantum-Compatible Systems under Non-Unitary Selection","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":"Quantum Causal Inference, Process Matrix, Non-Unitary Selection, State Tomography, Pseudo-Density Matrix, Quantum Fisher Information","lastPublishedDoi":"10.21203/rs.3.rs-8771353/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8771353/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We propose a novel framework for causal inference inspired by the process matrix formalism, where causal structure is not fixed but emerges through the act of observation. 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