Matrix separability preservation under conjugation

[nulll]

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

 

[nate808]

Hello nulll,

Thank you for your inquiry. I am familiar with the concept of matrix separability and its preservation under conjugation. There are a few papers that I can recommend on this topic:

1. "Preservation of Entanglement and Separability by Conjugation" by J. Eisert, K. Jacobs, P. Papadopoulos, and M.B. Plenio (Physical Review A, 2001)

2. "Preservation of Entanglement and Separability under Conjugation by the Clifford Group" by J. Eisert, K. Jacobs, P. Papadopoulos, and M.B. Plenio (Physical Review A, 2002)

3. "Preservation of Separability under Conjugation by the Clifford Group" by J. Eisert, K. Jacobs, P. Papadopoulos, and M.B. Plenio (Journal of Mathematical Physics, 2003)

These papers discuss the preservation of separability under conjugation in more detail and provide criteria for determining when a matrix will preserve separability. I hope these resources are helpful to you.