Ryu, Junghee Lee, Jinhyoung Ryu, Hoon 2025-09-22T03:00:42Z 2025-09-22T03:00:42Z 2025-09-16 2025-08 https://pubs.kist.re.kr/handle/201004/153207 We extend the generic Bell inequalities suggested by Son, Lee, and Kim [Phys. Rev. Lett. 96, 060406 (2006)] to incorporate multiple observables for tripartite systems and introduce a geometric methodology for calculating classical upper bounds of the inequalities. Our method transforms the problem of finding the classical upper bounds into identifying constraints in linear congruence relations. Using this approach, we derive the upper bounds for scenarios with three and four observables per party. In order to demonstrate quantum violations, we employ Greenberger-Horne-Zeilinger entangled states that can achieve values exceeding the classical upper bounds, with the violation becoming more pronounced as the number of observables increases. English Nature Publishing Group An approach using geometric diagrams to generic Bell inequalities with multiple observables Article 10.1038/s41598-025-14814-2 1 Scientific Reports, v.15, no.1 Scientific Reports 15 1 Y scie scopus 001556314600009 2-s2.0-105013880965 Multidisciplinary Sciences Science & Technology - Other Topics Article VIOLATION