1. The problem statement, all variables and given/known data Consider a qubit in the state |v> ∈ ℂ^2. Suppose that a measurement of δn is made on the qubit. Show that the probability of obtaining the result "+1" in the measurement is equal to 0 if and only if |v> and |n,+> are orthogonal. 2. Relevant equations Inner product axioms |v>|w> are orthogonal if |v>|w> = 0 3. The attempt at a solution First things first, that this is a if and only if proof. a. Prob(+1) = 0 implies that |v> and |n,+> are orthogonal b. |v> and |n,+> are orthogonal implies Prob(+1) = 0 Proof of b: Prob(+1) = | |n,+> |v> |^2 , but since |n,+> and |v> are orthogonal as assumed, by definition of orthogonality, this is equal to 0. And so Prob(+1) = 0. Proof of a: Similarly, Prob(+1) = | |n,+> |v> |^2 and since this equals 0, we see that |n,+>|v> = 0. But this is precisely the definition of orthogonality. My concern: My concern is mainly with the proof of a, it seems very weak. Would you consider this a proper proof?