A family of multipartite separability criteria based on correlation tensor

Abstract

A family of separability criteria based on correlation matrix (tensor) is provided. Interestingly, it unifies several criteria known before like e.g. CCNR or realignment criterion, de Vicente criterion and derived recently separability criterion based on SIC POVMs. It should be stressed that, unlike the well known Correlation Matrix Criterion or criterion based on Local Uncertainty Relations, the new criteria are linear in the density operator and hence one may find new classes of entanglement witnesses and positive maps. Interestingly, there is a natural generalization to multipartite scenario using multipartite correlation matrix. We illustrate the detection power of the above criteria on several well known examples of quantum states.

arXiv comment8 pages, 1 figure, comments welcome

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• A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices
• Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System
• Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses
• Bipartite Bound Entanglement
• On the Fidelity Robustness of CHSH--Bell Inequality via Filtered Random States
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• An Effective Way to Determine the Separability of Quantum State
• Group-Theoretic Perspective on the PPT and Realignment Criteria in the Magic Simplex for Bipartite Qutrits
• On the characterization of partially entanglement breaking and annihilating channels
• Inter-qubit correlation dynamics driven by mutual interactions