Question

Rewrite 13√|0⟩+2√3√|1⟩ in the sign basis.

Answer 1

(1+sqrt(2))/sqrt(6)|+> + (1-sqrt(2))/sqrt(6)|->

Answer 2

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.)