Identifying quantum resources in convex resource theories with Kirkwood-Dirac quasiprobabilities
Phys. Rev. A 111, 062217 – Published 25 June, 2025
DOI: https://doi.org/10.1103/htcg-9cv2
Abstract
We show that the Kirkwood-Dirac quasiprobability distributions can detect the presence of quantum resources in all convex resource theories via strictly negative probability outcomes. This negativity serves not only as a hallmark of resourcefulness in such theories, but also quantifies the geometric distance between a resourceful state and its closest free (i.e., nonresourceful) counterpart. Moreover, we demonstrate that these distributions can be rendered informationally complete, providing both a comprehensive description of the quantum state and a direct indicator of the underlying resource. We further discuss the relationship between convex resource theories, between strong anomalous weak values, and negative quasiprobabilities. Finally, by showing that negativity emerges only under measurement incompatibility, our results identify measurement incompatibility as a fundamental mechanism enabling quantum advantage in resourceful states.
