Moment Problem and Homodyne Detection

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We describe the measurement statistics of the balanced homodyne detection scheme in terms of the moment operators of the associated positive operator measures. In particular, we give a mathematically rigorous proof for the fact that the high amplitude limit in the local oscillator leads to a measurement of a rotated quadrature operator of the signal _eld. Using these results, we also show that each covariant phase space observable can be measured with the eight-port homodyne detector.