Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the (171)Yb(+) ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump technique. Qutrits constitute the most fundamental system to show quantum contextuality and our experiment represents the first one that closes the detection efficiency loophole for experimental tests of quantum contextuality in such a system.
We introduce a method to test the state-independent contextuality using a single copy of a system and without a state preparation. It can be implemented in realistic setups, like ion traps, or in other scenarios in which measurements are nondestructive. In particular, we show how to apply our idea to the Peres-Mermin state-independent contextuality test designed for nine observables of two spin-
1/2 particles. Each measurement round is performed on a postmeasurement state from the previous round. The sequence of measurements can be described as a Markov chain, and we observe that after a few rounds the system arrives at a stationary state to which the contextuality of the system can be attributed. However, it has to be noted that it does not depend on the initial state of the system and therefore it is not a property of a particular state preparation. Finally, we show that our approach to test contextuality admits noisy measurements as it implies the self-correction of possible detection errors present in any real experiments.
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.