  A reasonable quantum information theory for fermions must respect the parity
super-selection rule to comply with the special theory of relativity and the
no-signaling principle. This rule restricts the possibility of any quantum
state to have a superposition between even and odd parity fermionic states. It
thereby characterizes the set of physically allowed fermionic quantum states.
Here we introduce the physically allowed quantum operations, in congruence with
the parity super-selection rule, that map the set of allowed fermionic states
onto itself. We first introduce unitary and projective measurement operations
of the fermionic states. We further extend the formalism to general quantum
operations in the forms of Stinespring dilation, operator-sum representation,
and axiomatic completely-positive-trace-preserving maps. We explicitly show the
equivalence between these three representations of fermionic quantum
operations. We discuss the possible implications of our results in
characterization of correlations in fermionic systems.
