Greenberger-Horne-Zeilinger theorem cannot be extended to a Bell state
Greenberger-Horne-Zeilinger theorem cannot be extended to a Bell state
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DOI：
10.1103/physreva.68.052106
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发表时间：
2003-11
影响因子：
2.9
通讯作者：
Zeqian Chen
中科院分区：
文献类型：
--
作者：
Zeqian Chen
Greenberger-Horne-Zeilinger (GHZ) 定理通过使用三个量子位的最大纠缠态，展示了 Ernstein、Podelsky 和 Rosen 的局域实在论与量子力学之间的“全与无”矛盾。然而，本文表明，对于两个量子位的任何纠缠态（包括贝尔态），GHZ 证明的扩展是不可能的。该证明是通过证明两个量子位的一组相互交换的非局部自旋可观测量中不超过三个不同元素（除了不同的符号）这一事实而获得的。这也导致了双量子位系统的科亨-斯佩克定理的通用设置。
The Greenberger-Horne-Zeilinger (GHZ) theorem exhibits an "all versus nothing" contradiction between Ernstein, Podelsky, and Rosen's local realism and quantum mechanics by using a maximally entangled state of three qubits. However, it is shown in this paper that no extension of GHZ's proof is possible for any entangled state of two qubits, including Bell states. The proof is obtained by showing the fact that there are no more than three distinct elements (except for a different sign) in a set of mutually commuting nonlocal spin observables of two qubits. This also leads to a generic setup of the Kochen-Specker theorem for the two-qubit system.