Characterizing high-dimensional quantum contextuality

As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks. The dimension-dependent feature of quantum contextuality is known ever since its discovery, but there is still a lack of systematic methods for characterizing this fundamental feature. In this work, we propose a systematic and reliable method for certifying the high-dimensional advantages of quantum contextuality. In theory, our work gives a complete characterization of the dimension-constrained quantum contextual behavior, and particularly its nonconvex structure is revealed. In application, our method can be used for dimensionality certification of quantum information processing systems, and also for concentrating the quantum contextual behavior into lower-dimensional systems.