Hey all, I'm a beginner of the Quantum Computation and Quantum Information. For a long time, I feel very confuse about the question bellow. Could you do me a favor and show me the proof? Many thanks! Question: Show that any qubit can be expressed as psi=exp(iγ)[cos(θ/2)0+exp(iΦ)sin(θ/2)1] for real numbers γ,θ and Φ. The phase factor exp(iγ) has no observational effect and can be dropped. And then show that there is a one to one correspondence between qubits psi=cos(θ/2)0+exp(iΦ)sin(θ/2)1 and the points on the unit sphere in R(3) called the Bloch sphere, with and as the spherical coordinates of a point of the sphere.