Problem 1. Consider a single qubit and three experiments being performed on the single qubit: (A) The qubit is measured in X basis, and the outcome of the measurement is reported. (B) The qubit is first measured in the Z basis, and the experiment is continued only if +1 is the outcome. Now, the qubit is measured in the X basis, and the outcome of measurement is reported. (C) The qubit is measured in the Z basis, and the outcome of the measurement is discarded. The qubit is measured in the X basis, and the outcome of the measurement is reported. Calculate the probability of the measurement outcomes in experiments A to C if the qubit was initially in (a) pure state (7) = (10) + v21))/ V3, (b) mixed state p = (10) (0| + 2 |1) (11)/3. By comparing B and C, explain why discarding the measurement or observing it makes a difference on the subsequent measurement outcomes