= Solution
An <entangling gate> is a <unitary transformation> $U$ on two <quantum systems> for which \b[at least one pure product input has an entangled output]:
$$
\boxed{\exists\,|u\rangle_A,|v\rangle_B:\quad
U(|u\rangle_A\otimes|v\rangle_B)\ \text{is entangled}.}
$$
It need not create <quantum entanglement> on every <product state>. For example, the <controlled-NOT gate> leaves $|00\rangle$ a <product state> but maps $|+\rangle|0\rangle$ to a <Bell state>, so it is an <entangling gate>.
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