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

TL;DR

This paper introduces a minimal-measurement self-testing protocol for maximally entangled qudit states, enabling device-independent certification and unbounded randomness expansion with optimal measurement efficiency.

Contribution

It presents the first self-testing scheme for maximally entangled qudit states using only two measurements per subsystem, advancing device-independent quantum certification.

Findings

Achieves self-testing of maximally entangled states of arbitrary local dimension.

Requires only two measurements per subsystem for certification.

Enables unbounded randomness expansion with minimal measurement settings.

Abstract

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.