  Among the most fundamental questions in the manipulation of quantum resources
such as entanglement is the possibility of reversibly transforming all resource
states. The key consequence of this would be the identification of a unique
entropic resource measure that exactly quantifies the limits of achievable
transformation rates. Remarkably, previous results claimed that such asymptotic
reversibility holds true in very general settings; however, recently those
findings have been found to be incomplete, casting doubt on the conjecture.
Here we show that it is indeed possible to reversibly interconvert all states
in general quantum resource theories, as long as one allows protocols that may
only succeed probabilistically. Although such transformations have some chance
of failure, we show that their success probability can be ensured to be bounded
away from zero, even in the asymptotic limit of infinitely many manipulated
copies. As in previously conjectured approaches, the achievability here is
realised through operations that are asymptotically resource non-generating,
and we show that this choice is optimal: smaller sets of transformations cannot
lead to reversibility. Our methods are based on connecting the transformation
rates under probabilistic protocols with strong converse rates for
deterministic transformations, which we strengthen into an exact equivalence in
the case of entanglement distillation.
