> *On the [[Bloch Sphere]], we have $\ket 0, \ket 1$ on the north and south poles of the sphere respectively, with 180 degrees between them. But in reality, in the [[Hilbert Space]], these two states are orthogonal, with 90 degrees between them. Therefore, does this mean that one shouldn't regard the Bloch sphere as a valid basis for our system and that it's just partially-adequate visualization aid?* ------------------ Angles on the Bloch sphere are twice as big as in the Hilbert Space - For a general state, $\theta$ on the sphere corresponds to $\theta/2$ in the Hilbert Space. **This ensures a 1-1 mapping!**