  Although it is well known that the amount of resources that can be
asymptotically distilled from a quantum state or channel does not exceed the
resource cost needed to produce it, the corresponding relation in the
non-asymptotic regime hitherto has not been well understood. Here, we establish
a quantitative relation between the one-shot distillable resource yield and
dilution cost in terms of transformation errors involved in these processes.
Notably, our bound is applicable to quantum state and channel manipulation with
respect to any type of quantum resource and any class of free transformations
thereof, encompassing broad types of settings, including entanglement, quantum
thermodynamics, and quantum communication. We also show that our techniques
provide strong converse bounds relating the distillable resource and resource
dilution cost in the asymptotic regime. Moreover, we introduce a class of
channels that generalize twirling maps encountered in many resource theories,
and by directly connecting it with resource quantification, we compute
analytically several smoothed resource measures and improve our one-shot
yield--cost bound in relevant theories. We use these operational insights to
exactly evaluate important measures for various resource states in the resource
theory of magic states.
