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We define a positive operator valued measure $E$ on $[0,2\pi]\times R$describing the measurement of randomly sampled quadratures in quantum homodynetomography, and we study its probabilistic properties. Moreover, we give amathematical analysis of the relation between the description of a state interms of $E$ and the description provided by its Wigner transform.

Quantum Homodyne Tomography as an Informationally Complete Positive Operator Valued Measure