Entanglement quantification made simpler through hypothesis testing
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Subjects PhysicsQuantum information Understanding how to optimally detect and extract quantum entanglement typically involves intractable formulae that require optimization over many copies of quantum states. A shift of perspective leads to a much simpler formula based on the quantum relative entropy of a single quantum state, made possible by a new result in quantum state discrimination. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution Access options Access through your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any time Learn more Subscribe to this journal Receive 12 print issues and online access $259.00 per year only $21.58 per issue Learn more Buy this articlePurchase on SpringerLinkInstant access to the full article PDF.USD 39.95Prices may be subject to local taxes which are calculated during checkout Fig. 1: Entanglement testing and distillation. ReferencesVollbrecht, K. G. H. & Werner, R. F. Entanglement measures under symmetry. Phys. Rev. A 64, 062307 (2001). A study that shows the non-additivity of the relative entropy of entanglement, meaning that it cannot be computed using just a single copy.Article ADS Google Scholar Hastings, M. B. Superadditivity of communication capacity using entangled inputs. Nat. Phys. 5, 255–257 (2009). This article shows that entanglement generally leads to non-additivity, both in quantum communication and in entanglement theory itself.Article Google Scholar Horodecki, R., Horodecki, P., Horodecki, M. & Horodecki, K. Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009). A review article that gives an overview of the ways to quantify entanglement and the difficulties associated with it.Article ADS MathSciNet Google Scholar Brandão, F. G. S. L. & Plenio, M. B. Entanglement theory and the second law of thermodynamics. Nat. Phys. 4, 873–877 (2008). This work shows a deep connection between axiomatic entanglement manipulation and quantum hypothesis testing.Article Google Scholar Lami, L. A solution of the generalized quantum Stein’s lemma. IEEE Trans. Inf. Theory 71, 4454–4484 (2025). The paper introduces a key technique for composite quantum hypothesis testing that we rely on in our study.Article ADS MathSciNet Google Scholar Download referencesAdditional informationPublisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.This is a summary of: Lami, L. et al. Asymptotic quantification of entanglement with a single copy. Nat. Phys. https://doi.org/10.1038/s41567-026-03182-x (2026).Rights and permissionsReprints and permissionsAbout this articleCite this article Entanglement quantification made simpler through hypothesis testing. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03186-7Download citationPublished: 13 March 2026Version of record: 13 March 2026DOI: https://doi.org/10.1038/s41567-026-03186-7Share this articleAnyone you share the following link with will be able to read this content:Get shareable linkSorry, a shareable link is not currently available for this article.Copy shareable link to clipboard Provided by the Springer Nature SharedIt content-sharing initiative Asymptotic quantification of entanglement with a single copy Ludovico LamiMario BertaBartosz Regula Nature Physics Article Open Access 13 Mar 2026