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Featured Article

In the case of systems composed of \; m>2 subsystems the definition of separable and entangled states is richer than in the bipartite case. Indeed, in the multipartite case, apart from fully separable and fully entangled states, there also exists the notion of partial separability.

The definitions of fully separable and fully entangled multipartite states naturally generalizes that of separable and entangled states in the bipartite case, as follows.

Definition [Full \; m-partite separability (\; m-separability) of \; m systems]: The state \; \varrho_{A_1\ldots A_m} of \; m subsystems \; A_1, \ldots, A_m with Hilbert space \; \mathcal{H}_{A_1 \ldots A_m}=\mathcal{H}_{A_1}\otimes\ldots\otimes \mathcal{H}_{A_m} is fully separable if and only if it can be written in the form

\; \varrho_{A_1\ldots A_m} = \sum_{i=1}^k p_i \varrho_{A_1}^i \otimes \ldots \otimes \varrho_{A_m}^i.

Correspondingly, the state \; \varrho_{A_1\ldots A_m} is fully entangled if it cannot be written in the above form.

Read more about the Multipartite entanglement


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