The degree of entanglement between two spin1/2 particles can be assessed by performing a partial trace over one particle and evaluating the \"purity\" of the remaining state, where higher purity means lower entanglement. (a) Show that, for a general pure state of two identical spin1 / 2 particles, that the purity of the remaining state (and thus the measure of entanglement) does not depend on whether you trace over particle #1 or #2. (b) What is the purity of the remaining state, and thus the degree of entanglement, for the two particle state MIL)? (c) What is the purity of the remaining state, and thus the degree of entanglement, for the two particle state 1/\\/[| N) + | JD]? (d) What is the purity of the remaining state, and thus the degree of entanglement, for the two particle state 1/2llTi)+ \\m ITT>- lib]? (e) Explain the result you obtain in (d)