Ok, I have read a lot of material online to suggest that in Quantum Mechanics the Bloch Sphere = the Riemann Sphere = complex projective line.

I need to try to prove a bijective relationship between a two-dimensional Hilbert Space (i.e, ) and the complex projective line. Now here is what I know:

A projective hilbert space is noted: . So for we have . This is the complex projective line.

The way I understand it, an element of is , and an element of is .

How do I go about showing 1-1 and onto?