Experimental verification of quantum contextuality using a weak measurement in a single trapped ion

Quantum contextuality is usually verified through establishing the violation of appropriate inequalities constructed based on the assumption of generalized noncontextuality. Recently, the connection between anomalous weak values (AWVs) and the generalized contextuality under specific experimental conditions has been proposed. Experimentally, only the connection between the real part of the AWVs and the generalized contextuality is verified in a single-photon experimental system. In this paper, we conduct weak measurement experiments in a single 40Ca+ ion system under specific experimental conditions. The incompatibility between quantum mechanics and noncontextual ontological models (NCOMs) is verified by both the real and imaginary parts of the AWVs, which provides a more general test of the connection between the quantum contextuality and AWVs.