  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.
