One of the key issues in quantum discrimination problems is understanding the extent of the advantages in discrimination performance when using resource states compared to resourceless states. We show that in any resource theory of states, which may not be convex, the extent to which the maximum average success probability can be improved in quantum channel discrimination problems without using auxiliary systems can be precisely quantified by the robustness measure. This result offers an intuitive operational meaning of the robustness measure in any convex resource theory. Furthermore, we demonstrate that the robustness measure can also quantify the improvement in channel discrimination problems that use auxiliary systems. Using these findings, resources can be fully characterized to achieve higher success probabilities than any state without the given resource in channel discrimination problems.

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• Quantum information theory
• Resource theories