  We show that any quantum information theory based on anticommuting operators
must be supplemented by a superselection rule deeply rooted in relativity to
establish a reasonable notion of entanglement. While quantum information may be
encoded in the fermionic Fock space, the unrestricted theory has a peculiar
feature: The marginals of bipartite pure states need not have identical
entropies, which leads to an ambiguous definition of entanglement. We solve
this problem, by proving that it is removed by relativity, i.e., by the parity
superselection rule that arises from Lorentz invariance via the spin-statistics
connection. Our results hence unveil a fundamental conceptual inseparability of
quantum information and the causal structure of relativistic field theory.
