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.
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Loock et al. (2003) studied this question.
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