Device-independent bounds from Cabello's nonlocality argument

TL;DR

This paper extends Hardy's nonlocality argument to Cabello's version, demonstrating that maximum quantum violations are achieved by specific two-qubit states and measurements, and remains robust under small errors, enhancing device-independent quantum nonlocality tests.

Contribution

It generalizes Hardy's nonlocality argument to Cabello's case, showing the uniqueness of optimal states and measurements, and analyzes robustness to errors.

Findings

Maximum quantum violation achieved by a pure two-qubit state and projective measurements.

Optimal states and measurements are unique up to local isometries.

Maximum violation persists even with small errors in constraints.

Abstract

Hardy-type arguments manifest Bell nonlocality in one of the simplest possible ways. Except for demonstrating nonclassical signature of entangled states in question, they can also serve for device-independent self-testing of states, as shown, e.g., in Phys. Rev. Lett. 109, 180401 (2012). Here we develop and broaden these results to an extended version of Hardy's argument, often referred to as Cabello's nonlocality argument. We show that, as in the simpler case of Hardy's nonlocality argument, the maximum quantum value for Cabello's nonlocality is achieved by a pure two-qubit state and projective measurements that are unique up to local isometries. We also examine the properties of a more realistic case when small errors in the ideal constraints are accepted within the probabilities obtained and prove that also in this case the two-qubit state and measurements are sufficient for obtaining the maximum quantum violation of the classical bound.