Bloch sphere model for many spins?

1. Nov 19, 2009

Gerenuk

The Bloch sphere helps understanding the mathematical results for a one-spin state. One could think of the state as a spin pointing in direction $\hat{n}$. Then the probability for measureing the spin in the direction $\hat{m}$ is simply
$$P=|<\hat{m}|\hat{n}>|^2=\frac{1+\hat{n}\cdot\hat{m}}{2}$$
and that's all one need to know for one spin.

But what about multiple spins? How can I use a similar "Bloch-coordinate system" for more spins? In a way one only needs to know the scalar product? I came up with an expression but it's still quite complex.

Does any know an easier treatment of multiple spins but in terms of these "Bloch-coordinates"?