Three-outcome Bell inequalities tailored to many-body systems

We present a three-outcome Bell inequality which we show to be naturally suited to explore non- local correlations in many-body spin-1 systems or SU(3) models. From such an inequality, we show how simple bounds on single-particle observables can be used to construct Bell dimension witnesses, i.e., criteria whose violation signals the impossibility of reproducing the inferred correlations by Hilbert spaces of a certain dimension. In specific, our approach allows the use of violation depth to certify the number of genuine qutrits in an ensemble of arbitrary size. Next, we demonstrate that spin-nematic-squeezed correlations maximally violate the introduced criterion. These statistics naturally arise in spin-1 Bose-Einstein condensates and can be leveraged for sub-shot-noise multiphase estimation tasks. Finally, time permitting, I will comment on some intriguing connections between Bell nonlocality and quantum chaos, resulting from the eigenvalue spacing distribution of the Bell operator.

References:
A. Aloy, G. Müller-Rigat, J. Tura, M. Fadel, arXiv:2406.11792
A. Aloy, G. Müller-Rigat, M. Lewenstein, J. Tura, M. Fadel, arXiv:2406.11791
G. Müller-Rigat, A. Aloy, M. Lewenstein, M. Fadel, J. Tura, arXiv:2406.12823