三比特类GHZ态的Bell型不等式和非定域性

Bell-type inequality and tripartite nonlocality in three-qubit GHZ-class states

研究了一般形式类GHZ(Greenberger-Horne-Zeilinger)态的共生纠缠度及非定域性,给出了类GHZ纠缠态的共生纠缠、Mermin不等式和Svetlichny不等式的解析表达式,并通过数值计算讨论纠缠与非定域性之间的关系.结果表明,类GHZ纠缠态的共生纠缠和两个Bell型不等式描述的非定域性是一致的,Bell算符及其参量,能够明显展示量子态的非定域特性.

In this paper, we theoretically study the relation between concurrence and nonlocality depicted by Bell-type inequality violation of quantum mechanics prediction versus local realism prediction for the GHZ （Greenberger -Horne-Zeilinger） class states. Analytical expressions of concurrence, violations of the Mermin inequality and the Svetlichny inequality are obtained. Through numerical calcu- lations, the relationship between entanglement and nonlocality of GHZ-class states is discussed. Our results show that the concurrence is consistent with the degree of nonlocality described by violations of the two Bell-type inequalities of GHZ-class states. The Bell operator and its parameters can obviously reveal the nonlocal features of quantum states.