Device-independent bounds from Cabello's nonlocality argument

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.

arXiv comment8 pages, 1 figure, title slightly modified, close to published version

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• Quantum correlations on the no-signaling boundary: self-testing and more
• Self-testing of multiple unsharpness parameters through sequential violations of non-contextual inequality
• Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario
• Robust self-testing and certified randomness based on chained Bell inequality
• Bipartite polygon models: entanglement classes and their nonlocal behaviour