Understand
The difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking.
- We develop a general approach to this problem by introducing a new resource monotone that obeys a very strong type of monotonicity: it can rule out all transformations, probabilistic or deterministic, between states in any quantum resource theory.
- This allows us to place fundamental limitations on state transformations and restrict the advantages that probabilistic protocols can provide over deterministic ones, significantly strengthening previous findings and extending recent no-go theorems.
- We apply our results to obtain a substantial improvement in bounds for the errors and overheads of probabilistic distillation protocols, directly applicable to tasks such as entanglement or magic state distillation, and computable through convex optimization.