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We show that any essential application of an $n$-qubit C-SIGN or relatedquantum gate $G$ leaves its qubits everywhere entangled, provided they were noteverywhere 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) whenapplied to the same input state. By ``everywhere entangled'' we mean that thestate is not separable with respect to any bipartition of the qubits.

A note on the entangling properties of the C-SIGN and related quantum gates