  Nonlocal two-qubit quantum gates are represented by canonical decomposition
or equivalently by operator-Schmidt decomposition. The former decomposition
results in geometrical representation such that all the two-qubit gates form
tetrahedron within which perfect entanglers form a polyhedron. On the other
hand, it is known from the later decomposition that Schmidt number of nonlocal
gates can be either 2 or 4. In this work, some aspects of later decomposition
are investigated. It is shown that two gates differing by local operations
possess same set of Schmidt coefficients. Employing geometrical method, it is
established that Schmidt number 2 corresponds to controlled unitary gates.
Further, all the edges of tetrahedron and polyhedron are characterized using
Schmidt strength, a measure of operator entanglement. It is found that one edge
of the tetrahedron possesses the maximum Schmidt strength, implying that all
the gates in the edge are maximally entangled.
