Robust and versatile black-box certification of quantum devices

TL;DR

This paper introduces a semi-definite programming approach to enhance the robustness and versatility of black-box self-testing of quantum devices, enabling certification of complex quantum states with higher confidence.

Contribution

It develops a new method using semi-definite programming to improve robustness and extend self-testing to previously impossible quantum states.

Findings

A CHSH violation >2.57 certifies >70% singlet fidelity.

Enables robust self-testing of non-maximally entangled two-qutrit states.

Significantly improves robustness over previous self-testing schemes.

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.