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arXiv · 2203.09003

Self-Testing of a Single Quantum System: Theory and 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·Leong-Chuan Kwek
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Abstract

Certifying individual quantum devices with minimal assumptions is crucial for the development of quantum technologies. Here, we investigate how to leverage single-system contextuality to realize self-testing. We develop a robust self-testing protocol based on the simplest contextuality witness for the simplest contextual quantum system, the Klyachko-Can-Binicio\u{g}lu-Shumovsky (KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements (to an ideal configuration) as a function of the value of the witness under a pragmatic assumption on the measurements we call the KCBS orthogonality condition. We apply the method in an experiment with randomly chosen measurements on a single trapped $^{40}{\rm Ca}^+$ and near-perfect detection efficiency. The observed statistics allow us to self-test the system and provide the first experimental demonstration of quantum self-testing of a single system. Further, we quantify and report that deviations from our assumptions are minimal, an aspect previously overlooked by contextuality experiments.

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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, Leong-Chuan Kwek. 2022-03-17. Self-Testing of a Single Quantum System: Theory and Experiment. https://arxiv.org/abs/2203.09003

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