Study of Tangle on the Three Qubit Werner States by Using of Twirl Operation

In this paper we study the Tangle of three qubit Werner state using Twirl operation and association scheme. To do this, we introduce the invariants of Twirl operation using total spin representation. Then by using commutator property of this invariant with total spin, the general form of three qubit density matrix of Werner state is obtained. The restricted density matrix to the subspaces of the irreducible representations are diagonal(4x4) and Block(2x2). Then it provided that this given system has not Tangle. Finally, it is shown that common eigenvectors of this density matrix are equal to the idempotents of the group of association scheme S-3.