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.

中文翻译：

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来自 Cabello 非局部性参数的设备独立边界

Hardy 类型的论点以一种最简单的方式表明 Bell 非定域性。除了证明所讨论的纠缠态的非经典特征外，它们还可以用于独立于设备的状态自检，如Phys. 牧师莱特。 109, 180401 (2012)。在这里，我们将这些结果发展并扩展为 Hardy 论证的扩展版本，通常称为 Cabello 的非定域性论证。我们表明，与哈代非局域性论证的更简单情况一样，卡贝罗非局域性的最大量子值是通过纯双量子位状态和局部等距唯一的投影测量来实现的。我们还检查了在获得的概率范围内接受理想约束中的小错误时更现实情况的性质，并证明在这种情况下，双量子位状态和测量足以获得经典边界的最大量子违反。