Generation of bipartite spin entanglement via spin-independent scattering

We consider the bipartite spin entanglement between two identical fermions generated in spin-independent scattering. We show how the spatial degrees of freedom act as ancillas for the creation of entanglement to a degree that depends on the scattering angle $\theta$. The number of Slater determinants generated in the process is greater than 1, corresponding to genuine quantum correlations between the identical fermions. The maximal entanglement attainable of 1 ebit is reached at $\theta =\pi ∕2$. We also analyze a simple $\theta$-dependent Bell’s inequality, which is violated for $\pi ∕4<\theta ⩽\pi ∕2$. This phenomenon is unrelated to the symmetrization postulate but does not appear for unequal particles.

Figure 1

(Color online) Schematic picture of the two channels that contribute to the spin-independent scattering of two identical fermions. The shaded regions denote an arbitrary spin-independent interaction between the two fermions. The vertical arrows ↑, ↓ indicate the corresponding third component of spin.

Figure 2

(Color online) EOE $S\left(\theta \right)$ as a function of $\theta$.

Figure 3

(Color online) $F\left(\theta \right)$ as a function of $\theta$. The classical-quantum border corresponds to $F\left({\theta }_c\right)=1$, with ${\theta }_c=\pi ∕4$.