  We analyse the effect of bounding the occupation number of bosonic field
modes on the correlations among all the different spatial-temporal regions in a
setting in which we have a space-time with a horizon along with an inertial
observer. We show that the entanglement between A (inertial observer) and R
(uniformly accelerated observer) depends on the bound N, contrary to the
fermionic case. Whether or not decoherence increases with N depends on the
value of the acceleration a. Concerning the bipartition A-antiR (Alice with an
observer in Rindler's region IV), we show that no entanglement is created
whatever the value of N and a. Furthermore, AR entanglement is very quickly
lost for finite N and for infinite N. We will study in detail the mutual
information conservation law found for bosons and fermions. By means of the
boundary effects associated to N finiteness, we will show that for bosons this
law stems from classical correlations while for fermions it has a quantum
origin. Finally, we will present the strong N dependence of the entanglement in
R-antiR bipartition and compare the fermionic cases with their finite N bosonic
analogs. We will also show the anti-intuitive dependence of this entanglement
on statistics since more entanglement is created for bosons than for their
fermion counterparts.
