Tight bound on tilted CHSH inequality with measurement dependence

Runze Li, Dandan Li, Wei Huang, Bingjie Xu and Fei Gao

Physica A: Statistical Mechanics and its Applications, 2023, vol. 626, issue C

Abstract: Measurement dependence is the property that the distribution of the underlying variable is correlated with the measurement settings. If there is measurement dependence in a Bell test, the upper bound of Bell inequality will be affected. In the framework of device-independent quantum random number generation, the violation of Bell inequality indicates the existence of certified randomness. A tight upper bound on Bell inequality is critical to the amount of certified randomness. Recently, Sadhu and Das (2023) obtained a modified tilted CHSH inequality when measurement dependence exists. However, the upper bound of the modified tilted CHSH inequality they obtained is not tight. In this paper, we propose a method to quantify the measurement dependence applicable to the tilted CHSH inequality based on its structure. After that, we obtain a tight upper bound of modified tilted CHSH inequality and construct a local deterministic strategy to reach the upper bound.

Keywords: Quantum correlation; Bell nonlocality; Measurement dependence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123005927

DOI: 10.1016/j.physa.2023.129037

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