RECONSTRUCTING THE DENSITY-MATRIX OF A SPIN S THROUGH STERN-GERLACH MEASUREMENTS

The Pauli problem is solved for a spin of length s prepared in an arbi trary (unnormalized) mixed state which has (2s + 1)(2) free real param eters. The reconstruction of its density operator rho is possible if o ne knows the probabilities of the (2s + 1) spin components along each of (2s + 1) directions in space. These probabilties are directly acces sible through measurements performed with a Stem-Gerlach apparatus. A multipole expansion of the density operator establishes the link betwe en the matrix elements of rho and the measured intensities.