We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser–Horne–Shimony–Holt (CHSH) inequality. We make use of the elegant parametrization in the canonical form of these states, proposed by Meill and Meyer (Phys Rev A 96:062310, 2017) based on Majorana geometric representation. The reduced two-qubit states, extracted from an arbitrary pure entangled symmetric three-qubit state, do not violate the CHSH inequality, and hence, they are CHSH-local. However, when Alice and Bob perform a CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. We have also shown that two different families of three-qubit pure symmetric states, consisting of two and three distinct spinors (qubits), respectively, can be distinguished based on the strength of violation in the conditional CHSH nonlocality test. Furthermore, we identify six of the 46 classes of tight Bell inequalities in the three-party, two-setting, two-outcome, i.e., (3,2,2) scenario (López-Rosa et al. in Phys Rev A 94:062121, 2016). Among the two inequivalent families of three-qubit pure symmetric states, only the states belonging to three distinct spinor class show maximum violations of these six tight Bell inequalities.

我们使用Clauser-Horne-Shimony-Holt（CHSH）不等式探索了爱丽丝，鲍勃和查理之间共享的三比特纯对称状态的非局部性。我们根据Mejor和Meyer（Phys Rev A 96：062310，2017）根据马约拉纳邦的几何表示法，以这些状态的典范形式使用了优雅的参数化方法。从任意纯纠缠对称三量子位态中提取的简化的二量子位态不违反CHSH不等式，因此它们是CHSH局部的。但是，当爱丽丝和鲍勃执行CHSH测试时，在对查理的测量结果进行调节后，就会发现状态的非局部性。我们还表明，可以根据条件CHSH非局部性测试中的侵犯强度来区分分别由两个和三个不同的旋转子（量子位）组成的两个不同的三量子位纯对称状态族。此外，我们确定6的46类紧贝尔不等式的三方，双设定，双结局，即（3,2,2）情景（洛佩斯，罗莎等人在Phys修订版A 94： 062121，2016）。在三个三等位纯对称状态的两个不等价族中，仅属于三个不同的Spinor类的状态显示出对这六个紧密Bell不等式的最大违反。