We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multiparty multimode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence, a complete state determination, for example, by detecting the entire correlation matrix of a Gaussian state, is not needed.

• Received 27 December 2002

DOI:https://doi.org/10.1103/PhysRevA.67.052315