## Matrix separability preservation under conjugation!

Hello friends,
Someone know any paper about matrix separability preservation under conjugation? A well know result is that Clifford group preserve the Pauli group under conjugation, or in other words, $C_{4x4} (X_{2x2} \otimes X_{2x2}) C_{4x4}^{\dagger}$ will result in a 4x4 matrix in Pauli group, that also is a kronecker product of the other two 2x2 pauli matrices. Then, I'm find a critery to a matrix $U_{4x4}$ preserve the separability of another matrix, say $(V1_{2x2} \otimes V2_{2x2})$, by conjugation... Thus, $U_{4x4} (V1_{2x2} \otimes V2_{2x2}) U_{4x4}^{\dagger} = (J1_{2x2} \otimes J2_{2x2})$.

So, someone can help-me?

Thank's...

best regards,
nulll