{"paper_id":"1152b804-1a92-4e08-916f-ee047bfbc3a3","body_text":"Born-Rule Deviations Tested on Quantum Processors | 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PDF Research Article Born-Rule Deviations Tested on Quantum Processors Christian Balfagon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8579693/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract The Born rule, typically introduced as a quantum axiom, is shown to emerge as an equilibrium condition associated with modular (KMS) balance. We identify laboratory regimes where this balance can be weakly and controllably violated, and derive a universal, normalization-preserving correction to quantum measurement probabilities in the form of a modular exponential reweighting of Born amplitudes. The correction depends solely on experimentally reconstructed reduced states and outcome-resolved modular imbalance, and vanishes exactly under equilibrium, recovering the Born rule. We build a microscopic realization using standard von Neumann premeasurement, GKLS evolution of the apparatus, and projective readout, showing that the effect arises entirely within orthodox quantum mechanics without modifying unitary dynamics. The deviation leaves single-shot outcomes unchanged but induces a directed statistical bias visible only in large-N data. Locality and no-signalling hold, since in multipartite settings the correction depends only on the modular generator of the measured subsystem. We report experiments on IBM superconducting processors. First, full two-qubit Bell tomography confirms high-fidelity stabilizer correlations (E_ZZ, E_XX ≈ 0.98), validating reconstruction and establishing a Born-accurate baseline. Second, large-statistics three-qubit GHZ runs across multiple backends (ibm_fez, ibm_marrakesh, ibm_torino) show stable {000,111} sector frequencies under shot scaling, enabling extraction of preliminary modular tilt bounds. Finally, a controlled scaling study confirms 1/√N Born shot noise up to N = 20,000, while device biases remain roughly constant, establishing the metrological separation needed to detect nonequilibrium signatures. These results define a precision framework to estimate or constrain modular tilts on present-day platforms using raw (unmitigated) populations, tomography, and validated error models. They provide the first operational bounds on deviation parameters extracted from raw NISQ data in GHZ and Bell configurations, and outline a falsifiable protocol for future non-KMS driving experiments. The analysis explicitly separates statistical fluctuations from systematic bias through shot-scaling tests, enabling robust discrimination between equilibrium Born behavior and controlled nonequilibrium effects. This positions modular balance as an experimentally testable organizing principle linking quantum measurement statistics with nonequilibrium thermodynamics. Together, theory and data show that modular nonequilibrium deviations are experimentally accessible, tightly constrained, and operationally meaningful, suggesting that the Born rule may be the equilibrium shadow of a deeper thermodynamic structure in quantum theory. Born rule modular KMS balance quantum measurement GKLS nonequilibrium quantum systems superconducting qubits IBM Quantum Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryInformation.pdf Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 07 Apr, 2026 Reviewers agreed at journal 25 Feb, 2026 Reviewers invited by journal 23 Feb, 2026 Editor assigned by journal 14 Jan, 2026 Submission checks completed at journal 14 Jan, 2026 First submitted to journal 12 Jan, 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. We do this by developing innovative software and high quality services for the global research community. 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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-8579693\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":597207155,\"identity\":\"03ad9b17-2691-4df8-8052-da85825ee60b\",\"order_by\":0,\"name\":\"Christian Balfagon\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYBACPhjDgL0BRFoQ1sIG18JzAERKkKJFIgFEEaNFIvnw54qaO/Lmks+vbvhRIMHA396dQEBLWprkmWPPDHfOzim72QN0mMSZsxsIaMkxY2xgO5xgcDsn7QYPUIuBRC5BLcYfG/4Btdw8k3bzD5FaDCQb24BabrAfu02cLTzP0iQb+w4bbjiTw3ZbxkCCh6Bf+NmTD39s+HZY3uD48Wc33/yxkeNv78WvhUEgAcbiMQCT+JWDrTkAY7E/IKx6FIyCUTAKRiQAALuURvTV51lLAAAAAElFTkSuQmCC\",\"orcid\":\"\",\"institution\":\"University of Buenos Aires\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Christian\",\"middleName\":\"\",\"lastName\":\"Balfagon\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-01-12 09:23:19\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-8579693/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-8579693/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":104397758,\"identity\":\"49051f17-de8b-4016-a82b-d60a2c4aab5e\",\"added_by\":\"auto\",\"created_at\":\"2026-03-11 11:55:46\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":516173,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"Bornfinal.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8579693/v1_covered_3ef228f8-2bcf-4d09-ba8b-804d7c8e949e.pdf\"},{\"id\":103530842,\"identity\":\"ffcd2bd9-9ab4-48c6-b02e-e782e4a8024e\",\"added_by\":\"auto\",\"created_at\":\"2026-02-26 17:05:05\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":738463,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"SupplementaryInformation.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8579693/v1/7f09f1fd8b9e9ac4655178a9.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Born-Rule Deviations Tested on Quantum Processors\",\"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\":\"info@researchsquare.com\",\"identity\":\"quantum-information-processing\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"qinp\",\"sideBox\":\"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)\",\"snPcode\":\"11128\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11128/3\",\"title\":\"Quantum Information Processing\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"Born rule, modular KMS balance, quantum measurement, GKLS, nonequilibrium quantum systems, superconducting qubits, IBM Quantum\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-8579693/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8579693/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"The Born rule, typically introduced as a quantum axiom, is shown to emerge as an equilibrium condition associated with modular (KMS) balance. We identify laboratory regimes where this balance can be weakly and controllably violated, and derive a universal, normalization-preserving correction to quantum measurement probabilities in the form of a modular exponential reweighting of Born amplitudes. The correction depends solely on experimentally reconstructed reduced states and outcome-resolved modular imbalance, and vanishes exactly under equilibrium, recovering the Born rule.\\n\\nWe build a microscopic realization using standard von Neumann premeasurement, GKLS evolution of the apparatus, and projective readout, showing that the effect arises entirely within orthodox quantum mechanics without modifying unitary dynamics. The deviation leaves single-shot outcomes unchanged but induces a directed statistical bias visible only in large-N data. 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