Supplementary code for: Guillem Müller-Rigat, Albert Aloy, Maciej Lewenstein, Matteo Fadel and Jordi Tura, Three-outcome multipartite Bell inequalities: applications to dimension witnessing and spin-nematic squeezing in many-body systems, arXiv.2406.12823.

dimW

The folder contains the routines for the computation of the dimension-constrainted bound.

• bounds_qubit_Q.py variational bound and quantum bound. For the last, we employ ncpol2sdpa.
• PIBIout3qubits.m, PIBIout3qubits.m: applies the SDP relaxation according to the NV hierarchy supported in Matlab's package qdimsum.
• bounds_comparison.nb compares the bound with the maximal violation to construct Fig. 2 of the paper.

appW

The folder contains the verification of the witnesses and its application to the spin-1 Bose-Einstein condensate experiment.

• type2.nb addresses effective two-level witness Eq. 23 and Fig. 4 of the paper.
• type1.nb addresses three-level witness Eq. 28 and Fig. 5 of the paper.