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Tight bound on tilted CHSH inequality with measurement dependence

Author

Listed:
  • Li, Runze
  • Li, Dandan
  • Huang, Wei
  • Xu, Bingjie
  • Gao, Fei

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.

Suggested Citation

  • Li, Runze & Li, Dandan & Huang, Wei & Xu, Bingjie & Gao, Fei, 2023. "Tight bound on tilted CHSH inequality with measurement dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123005927
    DOI: 10.1016/j.physa.2023.129037
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    References listed on IDEAS

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    1. Antonio Acín & Lluis Masanes, 2016. "Certified randomness in quantum physics," Nature, Nature, vol. 540(7632), pages 213-219, December.
    2. Rodrigo Gallego & Lluis Masanes & Gonzalo De La Torre & Chirag Dhara & Leandro Aolita & Antonio Acín, 2013. "Full randomness from arbitrarily deterministic events," Nature Communications, Nature, vol. 4(1), pages 1-7, December.
    3. Peter Bierhorst & Emanuel Knill & Scott Glancy & Yanbao Zhang & Alan Mink & Stephen Jordan & Andrea Rommal & Yi-Kai Liu & Bradley Christensen & Sae Woo Nam & Martin J. Stevens & Lynden K. Shalm, 2018. "Experimentally generated randomness certified by the impossibility of superluminal signals," Nature, Nature, vol. 556(7700), pages 223-226, April.
    4. Yang Liu & Qi Zhao & Ming-Han Li & Jian-Yu Guan & Yanbao Zhang & Bing Bai & Weijun Zhang & Wen-Zhao Liu & Cheng Wu & Xiao Yuan & Hao Li & W. J. Munro & Zhen Wang & Lixing You & Jun Zhang & Xiongfeng M, 2018. "Device-independent quantum random-number generation," Nature, Nature, vol. 562(7728), pages 548-551, October.
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