Multisetting protocol for Bell correlated states detection with spin-f systems

We propose a multisetting protocol for the detection of two-body Bell correlations, and apply it to spin-nematic squeezed states realized in f pairs of SU(2) subsystems within spin-f atomic Bose–Einstein condensates. Experimental data for f=1, together with numerical simulations using the truncated Wigner method for f=1, 2, 3, demonstrate the protocol's effectiveness. We derive Bell inequalities tailored to collective observables of these subsystems and show how tuning interaction parameters controls the number of independent settings. Our findings extend multisetting Bell tests to high-spin ultracold ensembles, enabling scalable, flexible measurement configurations. This establishes a pathway to quantum metrology and information processing in tunable many-body platforms.