我們研究多體的糾纏態 (Greenberger-Horne-Zeilinger state, GHZ) 在隨機選取量測的情況下違反貝爾不等式 (Bell inequality) 的機率。受之前研究二體的相關工作啟發,我們關注如下的貝爾情境 (Bell scenario):在情境中的每一個參與者 (party) 會從三個互不偏差的量測基底 (mutually unbiased bases) 中選擇兩個作為他們的量測。而每個參與者的三個基底都是隨機且均勻的選。在這樣的情況下探討能不能夠違反貝爾不等式。我們的數值計算結果顯示在四體以上的情況,我們都可以找到一組量測(每個參與者三選二為一組)違反貝爾不等式(除了零測度集外,a set of measure zero)。
並且對白噪音 (white noise) 的忍受度高,這暗示了原則上在一個貝爾實驗中,可以不用建立共享座標系也能有非局域的特性。

We consider the problem of demonstrating non-Bell-local correlations by performing local measurements in randomly chosen bases on a multipartite Greenberger-Horne-Zeilinger
state. Inspired by previous work in the bipartite scenario, we consider specifically the case where each party performs measurements on bases that form a triad on the Bloch sphere.
As with the bipartite scenario, our numerical results for the tripartite, 4-partite, 5-partite and 6-partite scenario suggest that if each triad is randomly, but uniformly chosen according to the Haar measure, one always (except possibly for a set of measure zero) finds correlations that violate a Bell inequality. In addition, these quantum violations of a Bell inequality appear to be fairly resistant to white noise, indicating that such a demonstration can in principle be performed in an experimental situation without sharing a global reference frame.

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