Abstract

It is well known that the Q function which contains the complete information about the quantum state can be measured in a perfect eight-port homodyne detection scheme. A reconstruction formula for the density matrix elements in the photon number basis from a given Q function based on integrals rather than derivatives of the Q function has been recently derived [1]. In this paper we propose alternative schemes to reconstruct the photon statistics and density matrix, respectively, from double homodyne detection measurements. To this end the signal field is first split into two beams by a 50/50 beam splitter. Then the two output beams are directed on separate balanced homodyne detectors and the measured joint quadrature distribution P(x₁, x₂, Θ₁, Θ₂) for the quadrature components x₁ and x₂ belonging to the local oscillator phases Θ₁ and Θ₂ respectively, is considered. Note, that in our scheme the phases Θ_1,2 are adjustable independently from each other. In this sense we generalize the eight-port homodyne detection scheme for measurements of the Q function.

© 1998 IEEE