  We derive a general relation between the bosonic and fermionic entanglement
in the ground states of supersymmetric quadratic Hamiltonians. For this, we
construct canonical identifications between bosonic and fermionic subsystems.
Our derivation relies on a unified framework to describe both, bosonic and
fermionic Gaussian states in terms of so-called linear complex structures $J$.
The resulting dualities apply to the full entanglement spectrum between the
bosonic and the fermionic systems, such that the von Neumann entropy and
arbitrary Renyi entropies can be related. We illustrate our findings in one and
two-dimensional systems, including the paradigmatic Kitaev honeycomb model.
While typically SUSY preserves features like area law scaling of the
entanglement entropies on either side, we find a peculiar phenomenon, namely,
an amplified scaling of the entanglement entropy ("super area law") in bosonic
subsystems when the dual fermionic subsystems develop almost maximally
entangled modes.
