Self-testing protocols based on the chained Bell inequalities

TL;DR

This paper introduces self-testing protocols based on chained Bell inequalities, enabling certification of quantum states and measurements, including the entire plane of Pauli measurements, and certifying two bits of perfect randomness.

Contribution

It generalizes existing self-testing protocols by using chained Bell inequalities for multiple measurements, proving the uniqueness of the quantum state and measurements at maximal violation.

Findings

Maximal violation of chained Bell inequalities uniquely certifies quantum states and measurements.

In the large measurement limit, it self-tests the entire Pauli X-Z measurement plane.

Chained Bell inequalities can certify two bits of perfect randomness.

Abstract

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