Self-testing of a single quantum system from theory to experiment
Xiao‐Min Hu, Yi Xie, Atul Singh Arora, Ming-Zhong Ai, Kishor Bharti, Jie Zhang, Wei Wu, Ping-Xing Chen, Jin‐Ming Cui, Bi‐Heng Liu, Yun‐Feng Huang, Chuan‐Feng Li, Guang‐Can Guo, Jérémie Roland, Adán Cabello, L. C. Kwek
Abstract
Abstract Self-testing allows one to characterise quantum systems under minimal assumptions. However, existing schemes rely on quantum nonlocality 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-Binicioğlu-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 40 Ca + using randomly chosen measurements and perfect detection efficiency. Using the observed statistics, we obtain an experimental demonstration of self-testing of a single quantum system.