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Device-independent certification, also known as self-testing, aims atguaranteeing the proper functioning of untrusted and uncharacterized devices.For example, the quality of an unknown source expected to produce two-qubitmaximally entangled states can be evaluated in a bi-partite scenario, eachparty using two binary measurements. The most robust approach consists indeducing the fidelity of produced states with respect to a two-qubit maximallyentangled state from the violation of the CHSH inequality. In this paper, weshow how the self-testing of two-qubit maximally entangled states is improvedby a refined analysis of measurement statistics. The use of suitably chosenBell tests, depending on the observed correlations, allows one to concludehigher fidelities than ones previously known. In particular, nontrivialself-testing statements can be obtained from correlations that cannot beexploited by a CHSH-based self-testing strategy. Our results not only providenovel insight into the set of quantum correlations suited for self-testing, butalso facilitate the experimental implementations of device-independentcertifications.

Self-testing two-qubit maximally entangled states from generalized CHSH tests