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 (2s+1) spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by means of a standard Stern-Gerlach apparatus. To reconstruct a pure spin state is therefore possible on the basis of 3(2s+1) measured intensities.