Covariance measures of intermode correlations and inseparability for continuous variable quantum systems

Abstract

We introduce several coefficients characterizing the degree of intermode correlations and inseparability for multimode continuous variable quantum systems. All these coefficients are expressed either in terms of traces or determinants of the matrices (or their squares) formed from covariances of the quadrature components, or in terms of partial purities of the modes; thus they are more easy to use in calculations than frequently used entropic measures of entanglement. We compare the new and 'conventional' measures, considering two examples: (1) finite (pure) superpositions of coherent states (including multidimensional even and odd coherent states); (2) the evolution of generic (mixed and squeezed) Gaussian states of two resonantly coupled modes with the most general bilinear coupling in the cases of the nondegenerate parametric amplifier and the parametric converter.