Quantum resource theories (QRTs) provide a powerful framework for characterizing and quantifying quantum advantages in information processing. While most existing results focus on convex resource theories, many physically relevant resources such as non-Gaussianity and quantum discord naturally exhibit nonconvex structures. In this work, we conduct our study centered around projective robustness. We rigorously establish the dual representation of projective robustness via resource witnesses, which not only deepens the theoretical understanding of quantum resource quantification but also provides experimentally verifiable detection protocols for nonconvex resource theories. Moreover, we investigate the operational significance of projective robustness in general quantum resource theories without convexity constraints, revealing how projective robustness quantifies the advantage of resource states in simultaneous quantum channel discrimination and exclusion tasks. At last, we give an example of phase discrimination which shows that divergent projective robustness operationally quantifies quantum advantage in constrained phase discrimination, validated through qubit probes. We represent that resource states are more advantageous over free states in this example. Our results extend the applicability of projective robustness across both convex and nonconvex quantum resource theories, offering new perspectives on the fundamental limitations and potential of quantum resources in information processing.
Yang et al. (Fri,) studied this question.