One‑Shot Local Information at a Chiral Luttinger Liquid Edge: Capacity, Discrimination, and Recovery without Density Matrices

One‑Shot Local Information at a Chiral Luttinger Liquid Edge: Capacity, Discrimination, and Recovery without Density Matrices | 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 One‑Shot Local Information at a Chiral Luttinger Liquid Edge: Capacity, Discrimination, and Recovery without Density Matrices Andrei Tudor Patrascu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8391813/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 Local subsystems of gapless condensed‑matter phases—such as the chiral Luttinger liquid edge of the fractional quantum Hall effect—are described by type‑III von Neumann algebras, where reduced density matrices and von Neumann entropies do not exist. We develop an operational framework based on the categorical density matrix (CDM) that enables information‑theoretic computations directly on the local edge algebra $\A(\mathcal{O})$. For ensembles of weak coherent edge pulses, we derive an instrument‑independent one‑shot readout capacity via a closed‑form relative Holevo bound expressed purely in terms of the edge two‑point covariance and mean displacements, and show its monotone degradation under local quasi‑free (blur/noise) channels. We compute optimal one‑shot discrimination (Helstrom) using predual norms with tight fidelity/relative‑entropy bounds, and construct localized recovery (rotated Petz) with performance certified by the relative‑entropy gap. Finite‑resolution Gaussian instruments yield explicit outcome laws and selective updates, enabling adaptive protocols and quantifying post‑selection costs—tasks unavailable in density‑matrix or modular‑only approaches. A split‑window scheme connects these type‑III results to finite‑mode numerics with monotone convergence, providing a practical route to simulations for quantum Hall edge readout and related critical one‑dimensional systems. 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. 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