Operational advantages of projective robustness in nonconvex resource theories

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 through resource witness, 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. Our analysis also reveals how projective robustness quantifies the advantage of resourceful states in fundamental quantum processing tasks, extending beyond conventional convex-resource settings. At last, we give an example which shows that projective robustness effectively quantifies quantum advantage in phase discrimination with nonconvex and non-orthogonal free states. It adapts to nonconvex structures, captures the correlation between phase shift and quantum advantage, and satisfies Theorem 1’s tight lower bound conclusion. Generalized robustness, however, fails here due to its reliance on convex closure transformation. The results demonstrate the broad 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.