  We investigate the subadditivity of the bipartite entanglement entropy (EE)
of many-particle states, represented by Slater determinants, with respect to
single particle excitations. In this setting, subadditivity can be phrased as
erasure of EE, i.e. as a relative decrease in EE when adding excitations to the
quantum state. We identify sets of single particle states that yield zero EE if
jointly excited. Such states we dub entanglement erasing partner states (EEPS).
These EEPS reveal a mechanism that describes how to disentangle two subspaces
of a Hilbert space by exciting additional states. We demonstrate this general
finding in Anderson and many-body localized models. The studied concept of
entanglement erasure further enables us to derive the EE of Slater determinants
in the free tight binding model. Here, our analytical findings show
surprisingly good agreement with numerical results of the interacting XXX
chain. The described EEPS further impose a universal, i.e. model independent,
erasure of EE for randomly excited Slater determinants. This feature allows to
compute many-particle EE by means of the associated single particle states and
the filling ratio. This novel finding can be employed to drastically reduce the
computational effort in free models.
