Unitary local invariance
Abstract
Description
We address unitary local (UL) invariance of bipartite pure states. Given a bipartite state $|Ψ>>=\sum_{ij} ψ_{ij}\: |i>_1\otimes |j>_2$ the complete characterization of the class of local unitaries $U_1\otimes U_2$ for which $U_1\otimes U_2 |Ψ>>=|Ψ>>$ is obtained.The two relevant parameters are the rank of the matrix $Ψ$, $[Ψ]_{ij}=ψ_{ij}$, and the number of its equal singular values, {\em i.e.} the degeneracy of the eigenvalues of the partial traces of $|Ψ>>$.
Revised version. Accepted for publication Int. J. Quant. Inf
Revised version. Accepted for publication Int. J. Quant. Inf