2019/10/10 by Rouleux, Michel
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1910.04790
We are motivated by tripartite entanglement for fermions. While GHZ or W states involve 3-fold intrication, we consider here piecewise intrication of 3 fermions in \bf C2, namely of type ab+bc+ca. Before interaction with Stern-Gerlach apparatus, qu-bits are distinguishable; at the output however they turn into un-distinguishable particles, whose anti-symmetric wave function is of the form det(b-a,c-a) (affine determinant). More generally, d+1 intricated fermions in \bf Cd can be represented by the anti-symmetric wave function det(a1-a0,a2-a0,⋯,ad-a0). We investigate also properties of affine Slater determinants, as expectation values or reduced density matrices.