Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

Bell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit-qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, log 2d perfect random bits, while it requires only one random bit to encode the measurement choice.

Automated summary

Bell nonlocality as a resource for device-independent certification schemes has been extensively studied, and a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible has been proposed, which can achieve unbounded randomness expansion and log 2d perfect random bits with only one random bit required for encoding measurement choice.