Unitary local invariance
We address unitary local (UL) invariance of bipartite pure states. Given a bipartite state vertical bar Psi >> = Sigma ij psi ij(1)circle times vertical bar j >(2) the complete characterization of the class of local unitaries U-1 circle times U-2 for which U-1 circle times U-2 vertical bar Psi >>=vertical bar Psi >> is obtained. The two relevant parameters are the rank of the matrix Psi, [Psi](ij) = phi(ij), and the number of its equal singular values, i.e. the degeneracy of the eigenvalues of the partial traces of vertical bar Psi >>.
unitary local invariance entanglement