Discrete Q- and P-symbols for spin s

Non-orthogonal bases of projectors on coherent states are introduced to expand Hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a Hermitean operator (A) over cap in a family of (2s + 1)(2) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of (A) over cap at (2s + 1)(2) points on the unit sphere is already sufficient in order to recover the operator. This provides a straightforward method to reconstruct the mixed state of a spin since its density matrix is explicitly parametrized in terms of expectation values. Furthermore, a discrete P-symbol emerges naturally which is related to a basis dual to the original one.