Geometric extension of Clauser-Horne inequality to more qubitsopen access
- Authors
- Dutta, Arijit; Nahm, Tschang Uh; Lee, Jin hyoung; Zukowski, Marek
- Issue Date
- Sep-2018
- Publisher
- IOP PUBLISHING LTD
- Keywords
- geometric multiparty extension; CHinequality; Kolmogorov theory
- Citation
- NEW JOURNAL OF PHYSICS, v.20, pp.1 - 18
- Indexed
- SCIE
SCOPUS
- Journal Title
- NEW JOURNAL OF PHYSICS
- Volume
- 20
- Start Page
- 1
- End Page
- 18
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/149434
- DOI
- 10.1088/1367-2630/aadc78
- ISSN
- 1367-2630
- 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 circle plus B), where A circle plus B = (A - B) boolean OR (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 circle plus B circle plus C). We show that Mermin inequality can be retrieved from our extended CH inequality for three subsystems in a particular scenario. With our tripartiteCH 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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