6. Even though the Kraus representation gives an "internal" view of the dynamics of the open system Q, the Kraus operators contain some information about the environment. Concretely, let & be an evolution map with Kraus operators A,..., An, and p a state of Q. Define numbers Wkj = Tr(APA). (a) Show that if the initial state of E is pure (that is, 10)(0] for some unit vector 0)) and U(QE) is as in question 4, then the matrix [W] is the final density operator of E. (b) Suppose that Q is a qubit and the the Kraus operators for are al and bZ, where a,b R with a +62 1. First confirm that maps density operators to density operators. Second, find the eigenvalues of the final state of E when the p is one of 10X0, +X+, and 1.