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

Abstract

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 $f=1$, alongside with numerical simulations using the truncated Wigner method for $f=1,2,3$, demonstrate the effectiveness of the proposed protocol. Our findings extend the reach of multisetting Bell tests in ultracold atomic system, paving the way for extended quantum information processing in high-spin ensemble platforms.