Self-testing protocols based on the chained Bell inequalities

Abstract

Self testing is a device-independent technique based on non-local\ncorrelations whose aim is to certify the effective uniqueness of the quantum\nstate and measurements needed to produce these correlations. It is known that\nthe maximal violation of some Bell inequalities suffices for this purpose.\nHowever, most of the existing self-testing protocols for two devices exploit\nthe well-known Clauser-Horne-Shimony-Holt Bell inequality or modifications of\nit, and always with two measurements per party. Here, we generalize the\nprevious results by demonstrating that one can construct self-testing protocols\nbased on the chained Bell inequalities, defined for two devices implementing an\narbitrary number of two-output measurements. On the one hand, this proves that\nthe quantum state and measurements leading to the maximal violation of the\nchained Bell inequality are unique. On the other hand, in the limit of a large\nnumber of measurements, our approach allows one to self-test the entire plane\nof measurements spanned by the Pauli matrices X and Z. Our results also imply\nthat the chained Bell inequalities can be used to certify two bits of perfect\nrandomness.\n