Sum-of-squares decomposition for general bipartite Bell operators

Abstract The sum-of-squares (SOS) decomposition of Bell operators is a crucial tool for analyzing quantum correlations and verifying nonclassical behaviors. Building upon Gell-Mann’s generalization of Pauli matrices, we derive explicit forms for SOS decompositions of general Bell operators. We establish the minimal subsystem dimension required to represent Bell operators in specific tensor product spaces and obtain concrete decomposition expressions. Furthermore, we construct corresponding quantum states and measurement settings that exhibit quantum violations of classical bounds, with our approach extending naturally to isotropic states.