Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols

The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of states general resource-theoretic settings, often constituting unique monotone that relevant regime. We show this no longer case when one allows stochastic protocols may only succeed with some probability, which insufficient characterize rates state transformations, and new entropic quantity based on regularization Hilbert projective metric comes into play. Such scenario motivated by setting where cost associated transformations states, typically taken be number copies given state, instead identified size memory needed realize protocol. Our approach for constructing transformation achieve strictly higher than those imposed entropy. Focusing task resource distillation, we give broadly applicable strong converse bounds probabilistic distillation protocols, them tight settings such as entanglement nonentangling operations. This generalizes extends previously limitations are deterministic protocols. methods recent results one-shot well equipartition property