  Identifying what quantum-mechanical properties are useful to untap a superior
performance in quantum technologies is a pivotal question. Quantum resource
theories provide a unified framework to analyze and understand such properties,
as successfully demonstrated for entanglement and coherence. While these are
examples of convex resources, for which quantum advantages can always be
identified, many physical resources are described by a nonconvex set of free
states and their interpretation has so far remained elusive. Here we address
the fundamental question of the usefulness of quantum resources without
convexity assumption, by providing two operational interpretations of the
generalized robustness measure in general resource theories. First, we
characterize the generalized robustness in terms of a nonlinear resource
witness and reveal that any state is more advantageous than a free one in some
multicopy channel discrimination task. Next, we consider a scenario where a
theory is characterized by multiple constraints and show that the generalized
robustness coincides with the worst-case advantage in a single-copy channel
discrimination setting. Based on these characterizations, we conclude that
every quantum resource state shows a qualitative and quantitative advantage in
discrimination problems in a general resource theory even without any
specification on the structure of the free states.
