  In this work we consider two complex scalar fields distinguished by their
masses coupled to constant background electric and magnetic fields in the
$(3+1)$-dimensional Minkowski spacetime and subsequently investigate a few
measures quantifying the quantum correlations between the created
particle-antiparticle Schwinger pairs. Since the background magnetic field
itself cannot cause the decay of the Minkowski vacuum, our chief motivation
here is to investigate the interplay between the effects due to the electric
and magnetic fields. We start by computing the entanglement entropy for the
vacuum state of a single scalar field. Second, we consider some maximally
entangled states for the two-scalar field system and compute the logarithmic
negativity and the mutual information. Qualitative differences of these results
pertaining to the charge content of the states are emphasised. Based upon these
results, we suggest some possible effects of a background magnetic field on the
degradation of entanglement between states in an accelerated frame, for charged
quantum fields.
