Inefficient eight-port homodyne detection and covariant phase space observables

Abstract

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. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that the state distinguishing power of the observable is not affected by detector inefficiencies.

13 pages, 2 figures

References in corpus (2)

• A note on the measurement of phase space observables with an eight-port homodyne detector
• On the moment limit of quantum observables, with an application to the balanced homodyne detection

Cited by in corpus (2)

• The eight-port homodyne detector: the effect of imperfections on quantum random number generation and on detection of quadratures
• Asymmetry effects in homodyne and heterodyne measurements: Positive operator-valued measures and asymptotic security of Gaussian-continuous-variable quantum key distribution