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

TL;DR

This paper introduces a robust self-testing protocol for a single quantum system based on contextuality, demonstrated experimentally with trapped calcium ions, enabling device certification with minimal assumptions.

Contribution

It develops the first experimental self-testing method for a single quantum system using the KCBS inequality and minimal measurement assumptions.

Findings

Successfully self-tested a single quantum system experimentally.

Achieved near-perfect detection efficiency in the experiment.

Quantified minimal deviations from assumptions in the contextuality setup.

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.