  The emission of a pair of entangled photons by an electron in an intense
laser field can be described by two-photon transitions of laser-dressed,
relativistic Dirac--Volkov states. In the limit of a small laser field
intensity, the two-photon transition amplitude approaches the result predicted
by double Compton scattering theory. Multi-exchange processes with the laser
field, including a large number of exchanged laser photons, cannot be described
without the fully relativistic Dirac--Volkov propagator. The nonperturbative
treatment significantly alters theoretical predictions for future experiments
of this kind. We quantify the degree of polarization correlation of the photons
in the final state by employing the well-established concurrence as a measure
of the entanglement.
