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Under the assumption that every quantal measurement may give data about the post-measurement state of the inspected ensemble, the problem of the state determination is reconsidered. It is shown that orthogonal decomposition of the set of complex, n*n, Hermitian matrices into the commutative subsets allows operators to be found such that post-measurement information on these observables allows a partial (in some cases total) determination of the pre-measurement state to be effected.
I D Ivonovic (Tue,) studied this question.