A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist

A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist | 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 A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist Dariusz Chruscinski, Anidita Bera, Joonwoo Bae, Beatrix C. Hiesmayr This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6169028/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Aug, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Two approaches can be utilized to handle the separability problem, finding out whether a given bipartite qudit state is separable or not: a direct procedure on the state space or the effective tool of entanglement witnesses (EWs). This contribution studies the structure of EWs. Exploiting the very concept of mirrored EWs, increasing the detection power, we show, in contrast to the conjecture in a recent paper (Sci. Rep. 13, 10733 (2023)), there exist pairs of optimal EWs, which are both non-decomposible, i.e. can detect bound/PPT-entangled states in an optimal way. Since we show that the structure also extends to higher dimensions, our results reveal a further structure of entanglement witnesses. Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Aug, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 01 May, 2025 Reviews received at journal 31 Mar, 2025 Reviews received at journal 27 Mar, 2025 Reviewers agreed at journal 21 Mar, 2025 Reviewers agreed at journal 17 Mar, 2025 Reviewers invited by journal 17 Mar, 2025 Editor assigned by journal 17 Mar, 2025 Editor invited by journal 17 Mar, 2025 Submission checks completed at journal 14 Mar, 2025 First submitted to journal 06 Mar, 2025 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-6169028","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":431961753,"identity":"66a0e029-e3fb-44e9-8afa-a8179cc5926c","order_by":0,"name":"Dariusz Chruscinski","email":"","orcid":"","institution":"Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzi\\c{a}dzka 5/7, 87--100 Toru{\\'n}, Poland","correspondingAuthor":false,"prefix":"","firstName":"Dariusz","middleName":"","lastName":"Chruscinski","suffix":""},{"id":431961754,"identity":"efe17f70-fe32-4ed7-bf1e-91b389a69137","order_by":1,"name":"Anidita Bera","email":"","orcid":"","institution":"Department of Mathematics, Birla Institute of Technology Mesra, Jharkhand 835215, India","correspondingAuthor":false,"prefix":"","firstName":"Anidita","middleName":"","lastName":"Bera","suffix":""},{"id":431961756,"identity":"8bb385b8-687e-4603-a787-f8a2de9c8ff2","order_by":2,"name":"Joonwoo Bae","email":"","orcid":"","institution":"School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea","correspondingAuthor":false,"prefix":"","firstName":"Joonwoo","middleName":"","lastName":"Bae","suffix":""},{"id":431961757,"identity":"cac2f0b9-f125-4bf0-b541-a487c815e3dd","order_by":3,"name":"Beatrix C. 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