Self-Testing of a Single Quantum System: Theory and Experiment

Abstract Self-testing allows for characterising quantum systems under minimal assumptions. However, existing schemes rely on quantum non-locality and cannot be applied to systems that are not entangled. Here, we introduce a robust method that achieves self-testing of individual systems by taking advantage of contextuality. The scheme is based on the simplest contextuality witness for the simplest contextual quantum system—the Klyachko-Can-Binicioglu-Shumovsky inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements as a function of the value of the witness under a pragmatic assumption on the measurements. We apply the method in an experiment on a single trapped 40Ca+ and using randomly chosen measurements and perfect detection efficiency. Using the observed statistics, we obtain the first experimental demonstration of self-testing of a single quantum system with negligible deviations from the assumptions.