UNITARY LOCAL INVARIANCE
Matteo G. A. Paris · International Journal of Quantum Information · 2005
We address unitary local (UL) invariance of bipartite pure states. Given a bipartite state |Ψ〉〉 = ∑ij ψij |i〉1 ⊗ |j〉2 the complete characterization of the class of local unitaries U1 ⊗ U2 for which U1 ⊗ U2|Ψ〉〉 = |Ψ〉〉 is obtained. The two relevant parameters are the rank of the matrix Ψ, [Ψ]ij = ψij, and the number of its equal singular values, i.e. the degeneracy of the eigenvalues of the partial traces of |Ψ〉〉.