I see, you mean that I should consider also the appropriate element of area, which following your pointer should be:
(\sin{\theta_1})^{n-2}d\theta_1(\sin{\theta_2})^{n-3}d\theta_2 \ldots d\theta_{n-2} d\phi_1 d\phi_2\ldots d\phi_{n-1}
with 0\leq\theta_i\leq\pi and 0\leq\phi_i\leq 2\pi.
Hi Tom, I took a look, however the parametrization I need should be in the computational basis. What is wrong with:
|\phi\rangle=\cos\frac{\theta_1}{2}|0\rangle \\
+ e^{i\phi_1}\sin\frac{\theta_1}{2}\cos\frac{\theta_2}{2}|1\rangle \\
+...
I am not very sure that andrien parametrization suffices. Following mfb, dou you think that something of the following form works?
|\phi\rangle=\cos\frac{\theta_1}{2}|0\rangle
+ e^{i\phi_1}\sin\frac{\theta_1}{2}\cos\frac{\theta_2}{2}|1\rangle
+...
Thanks for your pointer. Probably my question was a little ambiguous. The thing is that I want to use the parametrization to integrate over the space of states, that's why I was looking for a generalization of spherical coordinates.
Any two dimensional state can be written as:
|\phi\rangle=\cos\frac{\theta}{2}|0\rangle+e^{i\phi}\sin\frac{\theta}{2}|1\rangle
where 0\leq\theta\leq\pi and 0\leq\phi\leq 2\pi, and 0\leq\theta\leq\pi. To pick one such state uniformly at random it suffices to draw \phi at random from its...