Tight constraints on probabilistic convertibility of quantum states

We develop two general approaches to characterising the manipulation of quantum states by means probabilistic protocols constrained limitations some resource theory. First, we give a necessary condition for existence physical transformation between states, obtained using recently introduced monotone based on Hilbert projective metric. In all affine theories (e.g. coherence, asymmetry, imaginarity) as well in entanglement distillation, show that provides and sufficient one-shot convertibility under resource-non-generating operations, hence no better restrictions are possible. use establish improved bounds performance both many-copy distillation protocols. Complementing this approach, introduce method bounding achievable probabilities transformations maps through family convex optimisation problems. it tightly characterise single-shot broad types theories, allowing an exact analysis trade-offs errors distilling maximally resourceful states. demonstrate usefulness our study distillation.