1. The problem statement, all variables and given/known data Find a state vector |v> ∈ ℂ^2 such that if a measurement of δx is made on a qubit in this state, then the prob. of obtaining the value of +1 in the measurement is 9/10. What is <δx> in this case? 2. Relevant equations State Vectors: https://en.wikipedia.org/wiki/Quantum_state 3. The attempt at a solution This problem seems somewhat simple to me, but I want to make sure I have the simple case down before moving forward. We seek to find a state vector that when taking a x-hat measurement results in a prob(+1) = 9/10 and thus a prob(-1) = 1/10. Therefore, if we let |v> = ( λ, μ ) then we know that prob(+1) = |λ+μ|^2/2 and prob(-1) = |λ-μ|^2/2 Since we know what these need to equal, it's clear to see that λ = 2/sqrt(5) and μ=1/sqrt(5) is a solution. Thus, <δx> is calculated as |α|^2-|β|^2 where α = (λ+μ)/sqrt(2) and β = (λ-μ)/sqrt(2). So, <δx> = 8/10=4/5. So, the state vector is thus 1/sqrt(5) (2,1). My concern is that I am not understanding the correct definition of state vector? Does a state vector 'have' any requirements that I am missing? Are my calculations correct?