Trade-off relations between measurement dependence and hidden information for factorizable hidden variable models
Abstract
The Bell theorem is explored in terms of a trade-off relation between underlying assumptions within the hidden variable model framework. In this paper, recognizing the incorporation of hidden variables as one of the fundamental assumptions, we propose a measure termed `hidden information' taking account of their distribution. This measure quantifies the number of hidden variables that essentially contribute to the empirical statistics. For factorizable models, hidden variable models that satisfy `locality' without adhering to the measurement independence criterion, we derive novel relaxed Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequalities. These inequalities elucidate trade-off relations between measurement dependence and hidden information in the CHSH scenario. It is also revealed that the relation gives a necessary and sufficient condition for the measures to be realized by a factorizable model.
Keywords
Cite
@article{arxiv.2208.13634,
title = {Trade-off relations between measurement dependence and hidden information for factorizable hidden variable models},
author = {Ryo Takakura and Kei Morisue and Issei Watanabe and Gen Kimura},
journal= {arXiv preprint arXiv:2208.13634},
year = {2025}
}