NOISY SIMULTANEOUS MEASUREMENT OF NONCOMMUTING OBSERVABLES IN 8-PORT AND 12-PORT HOMODYNE DETECTION

Classically eight- and twelve-port homodyne detectors can be used to m easure the Stokes parameters of a two-mode field simultaneously. We an alyse these schemes in the quantum case as approximate or noisy joint measurements of the noncommuting Stokes operators. The statistics of t he measurement are described in terms of these operators and noise. Th e twelve-port detector is also examined as allowing a noisy simultaneo us measurement of the quadratures and intensity of a one-mode field. T he vectors governing the statistics of the measurement are found. A si mple procedure for obtaining the Wigner function emerges.