On extension of the family of projections to positive operator-valued measure

The problem of constructing a measure on discrete set X taking values in positive cone bounded operators Hilbert space is considered. It assumed that projectionvalued function defined subset X0 the original initially given. aim study to find such scalar μ and continuation projector-valued from X, which results an operator-valued having density relative μ. In general, solved for |X| = 4 |X0| 2. As example, we consider takes projections coherent states. For this case, question information completeness measurement determined by constructed investigated. other words, it possible reconstruct quantum state (a unit trace operator) matrix product with state. shown restore only if projection. A restriction probability distribution also found, at can be obtained as result measuring certain