Ghose S, Sinclair N, Debnath S, Rungta P, Stock R
Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada.
Phys Rev Lett. 2009 Jun 26;102(25):250404. doi: 10.1103/PhysRevLett.102.250404. Epub 2009 Jun 25.
We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for three-qubit pure states in the Greenberger-Horne-Zeilinger class. We consider a family of states known as the generalized Greenberger-Horne-Zeilinger states and derive an analytical expression relating the three-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with three-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states does violate the Svetlichny inequality, and exactly analogous to the two-qubit case, the amount of violation is directly related to the degree of tripartite entanglement. We discuss further interesting properties of the generalized Greenberger-Horne-Zeilinger and maximal slice states.
我们分析了格林伯格-霍恩-泽林格（Greenberger-Horne-Zeilinger）类中三量子比特纯态的三方纠缠与真正的三方非定域性之间的关系。我们考虑一族被称为广义格林伯格-霍恩-泽林格态的态，并推导出一个解析表达式，该表达式将量化三方纠缠的三纠缠度与斯韦特利奇尼（Svetlichny）不等式联系起来，斯韦特利奇尼不等式是一种贝尔型不等式，只有当所有三个量子比特都非局域相关时才会被违背。我们表明，三纠缠度小于1/2的态不会违背斯韦特利奇尼不等式。另一方面，一族被称为最大切片态的态确实违背了斯韦特利奇尼不等式，并且与双量子比特情形完全类似，违背的程度与三方纠缠的程度直接相关。我们讨论了广义格林伯格-霍恩-泽林格态和最大切片态的进一步有趣性质。
