On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
arXiv:2205.02813 · doi:10.22331/q-2023-09-07-1103
Abstract
We show that the proof of the generalised quantum Stein's lemma [Brandão & 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 Brandão & 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 [Brandão & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brandão & 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.
arXiv comment29 pages; in v2 we added Section V.D and Section VI, and corrected several small typos; v5 contains minor corrections in the discussion in Section V
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