A Discrete Phase-Space Calculus for Quantum Spins based on a Reconstruction Method using Coherent States

To reconstruct a mixed or pure quantum state of a spin s is possible through coherent states: its density matrix is fixed by the probabilities to measure the value s along 4s(s+1) appropriately chosen directions in space. Thus, after inverting the experimental data, the statistical operator is parametrized entirely by expectation values. On this basis, a symbolic calculus for quantum spins is developed, the `expectation-value representation.' It resembles the Moyal representation for SU(2) but two important differences exist. On the one hand, the symbols take values on a discrete set of points in phase space only. On the other hand, no quasi-probabilities - that is, phase-space distributions with negative values - are encountered in this approach.