Problem 3. Let p be a density operator a minimum ensemble for p is an ensemble {(101, Mi : 2' E {1, 2. . . N }} of N elements such that N is the rank of p (Recall that rank(p) is the number of non-zero eigenvalues). (a) Calculate the single qubit density operator corresponding to the ensemble {(0.25,|0>,,>,(0.25,|0>,),(0.25,|1>,>,(0.250),); Is the given ensemble a minimum ensemble for the resulting density operator? If not, nd a minimum ensemble. (b) Repeat part (a) with the ensemble {(025, |0)x), (025, i200) + air/4 |1))) , (0.25, mm), (025, f 00> em\" I1) } 1 E