Quantum inference as an under-determined linear problem and the collectiveof accessible states

A detailed mathematical analysis of the collective of accessible micro-stat es compatible with a given set of a priori fixed expectation values (genera lized ensemble) is undertaken. To such an effect, the problem of quantum in ference is framed as an under-determined linear problem. The analysis is ba sed upon the splitting of the pertinent statistical distribution (the densi ty matrix one is trying to infer) into two orthogonal components. One of th e components happens to coincide with the minimum norm solution of the line ar problem posed by the fulfillment of the a priori conditions an the given expectation values. The remaining component belongs to the Null space of t he expectation values transformation. (C) 1999 Elsevier Science B.V. All ri ghts reserved.