Realistic eight-port homodyne detection and covariant phase space observables

: Lahti P, Pellonpaa JP, Schultz J

Publisher: TAYLOR & FRANCIS LTD

: 2010

: Journal of Modern Optics

: JOURNAL OF MODERN OPTICS

: J MOD OPTIC

: PII 925831079

: 13

: 57

: 13

: 1171

: 1179

: 9

: 0950-0340

DOI: https://doi.org/10.1080/09500340.2010.503013

We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement, that is, the measurement performed with fully efficient detectors. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that detector inefficiencies do not affect the observable's ability to distinguish between different states.