  There exist observational evidence to believe the existence of primordial
magnetic fields generated during inflation. We study primordial gravitational
waves (PGWs) during inflation in the presence of magnetic fields sustained by a
gauge kinetic coupling. In the model, not only gravitons as excitations of
PGWs, but also photons as excitations of electromagnetic fields are highly
squeezed. They become entangled with each other through graviton to photon
conversion and vice versa. We derive the reduced density matrix for the
gravitons and calculate their entanglement entropy. It turns out that the state
of the gravitons is not a squeezed state but a mixed state. Although witnessing
such an entanglement is not feasible at present, it would be an important
experimental challenge.
