  In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to
apply to some subjects in Quantum Computation and Mathematical Physics.
  The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action
is studied and generalized from a different point of view. Some problems are
also presented.
  In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes
entanglements in the case of $n=2$ is studied, and a clear-cut calculation of
the universal Yang-Mills action in (hep-th/0602204) is given for the abelian
case.
