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Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brand\u00e3o & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brand\u00e3o & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brand\u00e3o & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches.<\/jats:p>","DOI":"10.22331\/q-2023-09-07-1103","type":"journal-article","created":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T14:47:03Z","timestamp":1694098023000},"page":"1103","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":15,"title":["On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources"],"prefix":"10.22331","volume":"7","author":[{"given":"Mario","family":"Berta","sequence":"first","affiliation":[{"name":"Institute for Quantum Information, RWTH Aachen University, Aachen, Germany"},{"name":"Department of Computing, Imperial College London, London, UK"}]},{"given":"Fernando G. S. L.","family":"Brand\u00e3o","sequence":"additional","affiliation":[{"name":"Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA"},{"name":"AWS Center for Quantum Computing, Pasadena, CA, USA"}]},{"given":"Gilad","family":"Gour","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Institute for Quantum Science and Technology, University of Calgary, AB, Canada T2N 1N4"}]},{"given":"Ludovico","family":"Lami","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik und IQST, Universit\u00e4t Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany"},{"name":"QuSoft, Science Park 123, 1098 XG Amsterdam, The Netherlands"},{"name":"Korteweg\u2013de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, The Netherlands"},{"name":"Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands"}]},{"given":"Martin B.","family":"Plenio","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik und IQST, Universit\u00e4t Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany"}]},{"given":"Bartosz","family":"Regula","sequence":"additional","affiliation":[{"name":"Mathematical Quantum Information RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR) and RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan"},{"name":"Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan"}]},{"given":"Marco","family":"Tomamichel","sequence":"additional","affiliation":[{"name":"Center for Quantum Technologies, National University of Singapore, Singapore"},{"name":"Department of Electrical and Computer Engineering, College of Design and Engineering, National University of Singapore, Singapore"}]}],"member":"9598","published-online":{"date-parts":[[2023,9,7]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. 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