State of a particle pair produced by the Schwinger effect is not necessarily a maximally entangled Bell state

We analyze the spins of a Schwinger particle pair in a spatially uniform but time dependent electric field. The particle pair’s spins are in the maximally entangled Bell state only if the particles’ momenta are parallel to the electric field. However if transverse momentum is present, the spins are not in the maximally entangled Bell state. The reason is that the pair is created by the external field, which also carries angular momentum, and the particle pair can take away some of this external angular momentum.

Figure 1

Compton scattering in the center of mass frame. A right-handed photon collides with a right-handed electron. They turn almost completely backward. Their helicities are still both right handed. The total spin is not conserved, because the reflected waves are the p-waves, which take away angular momentum.