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We provide new methods for characterizing general closed and convex quantumresource theories, including dynamic ones, based on entropic concepts andoperational tasks. We propose a resource-theoretic generalization of thequantum conditional min-entropy, termed the free conditional min-entropy(FCME), in the sense that it quantifies an observer's ``subjective'' degree ofuncertainty about a quantum system given that the observer's informationprocessing is limited to free operations of the resource theory. Thisgeneralized concept gives rise to a complete set of entropic conditions forfree convertibility between quantum states or channels in any closed and convexquantum resource theory. It also provides an information-theoreticinterpretation for the resource global robustness of a state or a channel interms of a mutual-information-like quantity derived from the FCME. Apart fromthis entropic approach, we also characterize dynamic resources by analyzingtheir performance in operational tasks. Based on such tasks, we constructoperationally meaningful and complete sets of resource monotones, which enablefaithful tests of free convertibility between quantum channels. Finally, weshow that every well-defined robustness-based measure of a channel can beinterpreted as an operational advantage of the channel over free channels in acommunication task.

Entropic and operational characterizations of dynamic quantum resources