Robust and Versatile Black-Box Certification of Quantum Devices

TLDR

Self‑testing enables assessment of quantum states and measurements in a black‑box setting solely from observed statistics, yet only a few examples exist and they apply only to devices extremely close to ideal. The authors aim to extend self‑testing to more realistic devices by employing the semi‑definite programming hierarchy for quantum‑correlation characterization. They apply the SDP hierarchy to analyze quantum correlations, providing a systematic framework for certification. This method dramatically improves robustness, showing that a CHSH violation above 2.57 certifies a singlet fidelity exceeding 70 % and enabling robust self‑testing of non‑maximally entangled two‑qutrit states in the CGLMP scenario.

Abstract

Self-testing refers to the fact that, in some quantum devices, both states and measurements can be assessed in a black-box scenario, on the sole basis of the observed statistics, i.e. without reference to any prior device calibration. Only a few examples of self-testing are known, and they just provide non-trivial assessment for devices performing unrealistically close to the ideal case. We overcome these difficulties by approaching self-testing with the semi-definite programming hierarchy for the characterization of quantum correlations. This allows us to improve dramatically the robustness of previous self-testing schemes -e.g.: we show that a CHSH violation larger than 2.57 certifies a singlet fidelity of more than 70%. In addition, the versatility of the tool brings about self-testing of hitherto impossible cases, such as robust self-testing of non-maximally entangled two-qutrit states in the CGLMP scenario.