Suppose that a qubit is in the state |φ〉 = a|0〉 + 1 − a2 |1〉 where a ∈ [−1, 1]. If we �rst

Question

perform a standard basis measurement on this qubit and then perform a |u〉, |u⊥ 〉-basis mea-
√
surement where |u〉 = b|0〉 + 1 − b2 |1〉 for some b ∈ [−1, 1], what is the probability that the
outcome of the second measurement is u, in terms of a and b?