  We show that any essential application of an $n$-qubit C-SIGN or related
quantum gate $G$ leaves its qubits everywhere entangled, provided they were not
everywhere entangled to begin with. By ``essential'' we mean roughly that $G$
is not equivalent to a similar gate of smaller arity (or to the identity) when
applied to the same input state. By ``everywhere entangled'' we mean that the
state is not separable with respect to any bipartition of the qubits.
