Quorum of observables for universal quantum estimation

Quantum tomography is the process of reconstructing the ensemble average of an arbitrary operator (observable or not, including the density matrix), w hich may not be directly accessible by feasible detection schemes, starting from the measurement of a complete set of observables i.e. a quorum. The m easurement of a quorum thus represents a complete characterization of the q uantum state. The operator expression in terms of a quorum corresponds to a n expansion on an irreducible set of operators in the Liouville space. We g ive two general characterizations of these sets, and show that all the know n quantum tomographies can be described in this framework. New operatorial resolutions are also given that may be used in novel reconstruction schemes .