Question

Suppose that a qubit is in the state |ψ> = a |0> + √ (1-a^2)|1> where a [-1,1] . If we first perform a standard basis measurement on this qubit and then perform a |u>, |u⊥> -basis measurement where |u> = b |0> + √ (1-b^2)|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 ?

Answer 1

1+(2*a^2*b^2)-(a^2+b^2)