The effect on (2, N, 2) Bell tests with distributed measurement dependence

Bell tests, as primitive tools to detect nonlocality in bipartite systems, rely on an assumption, i.e., measurement independence. In practice, it is difficult to ensure measurement independence. It is necessary to investigate how Bell tests are affected by relaxing measurement independence. In the s...

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Bibliographic Details
Published in:	Quantum information processing 2020, Vol.19 (9), Article 339
Main Authors:	Li, Dan-Dan, Chen, Lin-Yan, Cao, Ya, Huang, Xiao-Hong, Gao, Fei, Ma, Yan
Format:	Article
Language:	eng
Subjects:	Caves Chains Correlation analysis Data processing Data Structures and Information Theory Dependence Inequalities Mathematical Physics Physics Physics and Astronomy Quantum Computing Quantum Information Technology Quantum phenomena Quantum Physics Spintronics Tightness Upper bounds
Online Access:	Get full text
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Summary:	Bell tests, as primitive tools to detect nonlocality in bipartite systems, rely on an assumption, i.e., measurement independence. In practice, it is difficult to ensure measurement independence. It is necessary to investigate how Bell tests are affected by relaxing measurement independence. In the simplest (2, 2, 2) CHSH Bell test which consists of two parties, two measurements per party and two possible outcomes per measurement, the results between the maximal value of CHSH correlation function and distributed measurement dependence (DMD) are given, where DMD is a general measure of relaxing measurement independence. However, in a general Bell scenario of an arbitrary number of measurements per party, i.e., (2, N , 2), pertinent results are still missing. To solve it, we establish the relations between the maximal value of (2, N , 2) Pearle–Braunstein–Caves (PBC) chain correlation function that maintains the locality and the degree of DMD, denoted as DMD-induced PBC chain inequalities. Furthermore, we show the tightness of these derived inequalities via constructing local hidden variable models that fake the upper bounds. Compared with the simplest CHSH Bell test, our derived inequalities need less amount of measurement dependence to fake the quantum prediction with N increasing, which is beneficial to analyze the security of device-independent quantum information processing tasks such as randomness expansion.
ISSN:	1570-0755 1573-1332