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

We show that the proof of the generalised quantum Steins lemma Brandão 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.