On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources

• URL: http://arxiv.org/abs/2205.02813v4
• Date: Fri, 25 Aug 2023 11:04:32 GMT
• Title: On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• Authors: Mario Berta, Fernando G. S. L. Brand\~ao, Gilad Gour, Ludovico Lami, Martin B. Plenio, Bartosz Regula, Marco Tomamichel
• Abstract summary: We show that the proof of the generalised quantum Stein's lemma is not correct due to a gap in the argument leading to Lemma III.9. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement.
• Score: 51.243733928201024
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that the proof of the generalised quantum Stein's lemma [Brand\~ao & Plenio, Commun. 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\~ao & 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\~ao & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brand\~ao & 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.

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