Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality

TL;DR

This paper introduces a new self-testing protocol using nonmaximal violations in Hardy's nonlocality test, enabling certification of all pure two-qubit entangled states except maximally entangled ones, thus advancing quantum device verification.

Contribution

It demonstrates that nonmaximal nonlocal correlations in Hardy's test can be used for self-testing, expanding beyond maximal violations and providing a complete characterization for almost all pure two-qubit states.

Findings

Nonmaximal Hardy correlations can self-test pure two-qubit states.

The protocol characterizes the boundary of quantum correlations.

It extends self-testing methods beyond maximal Bell violations.

Abstract

Self-testing protocols enable certification of quantum devices without demanding full knowledge about their inner workings. A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in Bell experiment known as Hardy's test of nonlocality not only the maximally nonlocal correlation self-tests a quantum state, rather a non-maximal nonlocal behavior can serve the same purpose. We, in fact, completely characterize all such behaviors leading to self-test of every pure two qubit entangled state except the maximally entangled ones. Apart from originating a novel self-testing protocol, our method provides a powerful tool towards characterizing the complex boundary of the set of quantum correlations.