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arXiv · 1803.07275

Geometric extension of Clauser-Horne inequality to more qubits

Arijit Dutta·Tschang-Uh Nahm·Jinhyoung Lee·Marek Żukowski
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Abstract

We propose a geometric multiparty extension of Clauser-Horne (CH) inequality. The standard CH inequality can be shown to be an implication of the fact that statistical separation between two events, $A$ and $B$, defined as $P(A\oplus B)$, where $A\oplus B=(A-B)\cup(B-A)$, satisfies the axioms of a distance. Our extension for tripartite case is based on triangle inequalities for the statistical separations of three probabilistic events $P(A\oplus B \oplus C)$. We show that Mermin inequality can be retrieved from our extended CH inequality for three subsystems. With our tripartite CH inequality, we investigate quantum violations by GHZ-type and W-type states. Our inequalities are compared to another type, so-called $N$-site CH inequality. In addition we argue how to generalize our method for more subsystems and measurement settings. Our method can be used to write down several Bell-type inequalities in a systematic manner.

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Arijit Dutta, Tschang-Uh Nahm, Jinhyoung Lee, Marek Żukowski. 2018-03-20. Geometric extension of Clauser-Horne inequality to more qubits. https://doi.org/10.1088/1367-2630%2Faadc78

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