Reconstructing a pure state of a spin s through three Stern-Gerlach measurements

Consider a spin s prepared in a pure state. It is shown that, generically, the moduli of the spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by means of a standard Stern-Gerlach apparatus. It is therefore possible to reconstruct a generic pure state on the basis of 6s independent measured intensities.