2024/11/27 by Songyi Liu, Yongjun Wang, Liu, Songyi +7
Chemistry · #FOS: Mathematics #FOS: Physical sciences #History and advancements in chemistry #Logic (math.LO) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2411.18146
openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial Boolean algebra to characterize the contextuality theory with local consistency and exclusivity, and then prove that the finite dimensional quantum systems are determined by atoms using two graph structure theorems. We also generalize our work to infinite dimensional cases. Our conclusions indicate that the quantum mechanics is a graph-structured combination of multiple hidden-variable theories, and provide a precise mathematical framework for quantum contextuality.