Experimental measurement of covariance matrix of two-mode entangled state

A two-mode entangled state was generated experimentally through mixing two squeezed lights from two optical parametric amplifiers on a 50/50 beam splitter. The entangled beams were measured by means of two pairs of balanced homodyne detection systems respectively. The relative phases between the local beams and the detected beams can be locked by using the optical phase modulation technique. The covariance matrix of the two-mode entangled state was obtained when the relative phase of the local beam and the detected beam in one homodyne detection system is locked and the other is scanned. This method provides a way by which one can extract the covariance matrix of any selected quadrature components of two-mode Gaussian state.