Quantum Homodyne Tomography as an Informationally Complete Positive Operator Valued Measure

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

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