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arXiv · 2208.13634

Trade-off relations between measurement dependence and hidden information for factorizable hidden variable models

Ryo Takakura·Kei Morisue·Issei Watanabe·Gen Kimura
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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.

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Ryo Takakura, Kei Morisue, Issei Watanabe, Gen Kimura. 2022-08-29. Trade-off relations between measurement dependence and hidden information for factorizable hidden variable models. https://doi.org/10.22331/q-2025-03-14-1662

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