# Matrix separability preservation under conjugation!?

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:

• $C(P_{1} \otimes P_{2})C^{\dagger} = P_{3} \otimes P_{4}$, with $C \in$ Clifford group and $P_{n} \in$ Pauli group.

Then, I'm searching by criteria and proofs that H, a subgroup of $SU(4)$, preserves the separability under conjugation of the J, a subgroup of $SU(2)$.

So, someone can help-me? Good related papers or books?

Thank's...

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What is matrix separability? – Qiaochu Yuan Sep 11 '12 at 20:58
A $SU(4)$ matrix is separable if it can be write as a kronecker product of two another $SU(2)$ matrices. – user901366 Sep 11 '12 at 21:19