  We address the task of compression of fermionic quantum information. Due to
the parity superselection rule, differently from the case of encoding of
quantum information in qubit states, part of the information carried by
fermionic systems is encoded in their delocalised correlations. As a
consequence, reliability of a compression protocol must be assessed in a way
that necessarily accounts also for the preservation of correlations. This
implies that input/output fidelity is not a satisfactory figure of merit for
fermionic compression schemes. We then discuss various aspects regarding the
assessment of reliability of an encoding scheme, and show that entanglement
fidelity in the fermionic case is capable of evaluating the preservation of
correlations, thus revealing itself strictly stronger than input/output
fidelity, unlike the qubit case. We then introduce a fermionic version of the
source coding theorem showing that, as in the quantum case, the von Neumann
entropy is the minimal rate for which a fermionic compression scheme exists,
that is reliable according to the entanglement fidelity criterion.
