Quantum operations in an information theory for fermions

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