Work

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

Year: 2025

Type: article

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.

Source: Quantum

DOI: 10.22331/q-2025-03-14-1662

Authors: Ryo Takakura, Kei Morisue, Issei Watanabe, Gen Kimura

Institutions: The University of Osaka, Waseda University, Shibaura Institute of Technology

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science, Co-creation place formation support program