  It is known from Schmidt decomposition that Schmidt number of nonlocal
two-qubit quantum gates is 2 or 4. We identify conditions on geometrical points
of a gate to have Schmidt number 2. A simple analysis reveals that Schmidt
number 2 corresponds to controlled unitary gates with CNOT being the only
perfect entangler. Further, it is shown that Schmidt strength and entangling
power are maximum only for CNOT in the controlled unitary family.
