Separability Criterion for multipartite quantum states based on the Bloch representation of density matrices

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dc.creatorHassan, Ali Saif M.
dc.creatorJoag, Pramod S.
dc.date2007-04-30
dc.date2008-04-13
dc.date.accessioned2026-07-07T09:50:33Z
dc.date.available2026-07-07T09:50:33Z
dc.descriptionWe give a new separability criterion, a necessary condition for separability of $N$-partite quantum states. The criterion is based on the Bloch representation of a $N$-partite quantum state and makes use of multilinear algebra, in particular, the matrization of tensors. Our criterion applies to {\it arbitrary} $N$-partite quantum states in $\mathcal{H}=\mathcal{H}^{d_1}\otimes \mathcal{H}^{d_2} \otimes ... \otimes \mathcal{H}^{d_N}.$ The criterion can test whether a $N$-partite state is entangled and can be applied to different partitions of the $N$-partite system. We provide examples that show the ability of this criterion to detect entanglement. We show that this criterion can detect bound entangled states. We prove a sufficiency condition for separability of a 3-partite state, straightforwardly generalizable to the case $N > 3,$ under certain condition. We also give a necessary and sufficient condition for separability of a class of $N$-qubit states which includes $N$-qubit PPT states.
dc.description23 pages no figures comments are welcome
dc.identifierhttps://arxiv.org/abs/0704.3942
dc.identifierhttp://arxiv.org/abs/0704.3942
dc.identifierQuantum Information and Computation, vol. 8, No. 8&9 (2008) 0773-0790
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164975
dc.subjectQuantum Physics
dc.titleSeparability Criterion for multipartite quantum states based on the Bloch representation of density matrices
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