Amplified quantum non-demolition measurements of optical quadratures using quadratic nonlinearity

Quantum non-demolition (QND) measurement is a special technique that allows to evade quantum back-action. In this paper, we propose a new QND measurement scheme of the optical field quadratures based on the non-degenerate optical parametric amplifier. We show that for a proper set of parameters, this scheme can realize a new type of QND measurement, where the quadrature of interest is amplified, but still does not subject to any back action.