Probabilistic Entanglement Distillation and Cost under Approximately Nonentangling and Dually Nonentangling Instruments
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Quantum Physics arXiv:2601.00383 (quant-ph) [Submitted on 1 Jan 2026] Title:Probabilistic Entanglement Distillation and Cost under Approximately Nonentangling and Dually Nonentangling Instruments Authors:Xian Shi View a PDF of the paper titled Probabilistic Entanglement Distillation and Cost under Approximately Nonentangling and Dually Nonentangling Instruments, by Xian Shi View PDF HTML (experimental) Abstract:Entanglement distillation and entanglement cost are fundamental tasks in quantum entanglement theory. This work studies both in the probabilistic setting and focuses on the asymptotic error exponent of probabilistic entanglement distillation when the operational model is $\delta$-approximately nonentangling(ANE) and $\delta$-approximately dually nonentangling(ADNE) quantum instruments. While recent progress has clarified limitations of probabilistic transformations in general resource theories, an analytic formula for the error exponent of probabilistic entanglement distillation under approximately (dually) nonentangling operations has remained unavailable. Building on the framework of postselected quantum hypothesis testing, we establish a direct connection between probabilistic distillation and postselected hypothesis testing against the set of separable states. In particular, we derive an analytical characterization of the distillation error exponent under ANE. Besides, we relate the exponent to postselected hypothesis testing with measurements restricted to be separable. We further investigate probabilistic entanglement dilution and establish a relation between probabilistic entanglement costs under approximately nonentangling and approximately dually nonentangling instruments, together with a bound on the probabilistic entanglement cost under nonentangling instruments Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.00383 [quant-ph] (or arXiv:2601.00383v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.00383 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Xian Shi [view email] [v1] Thu, 1 Jan 2026 16:20:06 UTC (47 KB) Full-text links: Access Paper: View a PDF of the paper titled Probabilistic Entanglement Distillation and Cost under Approximately Nonentangling and Dually Nonentangling Instruments, by Xian ShiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)