Question

We have a qubit in the state |ϕ⟩=3√2|0⟩+12|1⟩, which we want to measure in the {cosθ|0⟩+sinθ|1⟩,sinθ|0⟩−cosθ|1⟩} basis. In order for the two possible outcomes to be equiprobable, what should be the value of θ in degrees? (Answer between 0 and 90.)

Answer 1

75