Quantum Separability Criteria for Arbitrary Dimensional Multipartite States

Abstract

We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our criteria are more powerful than the positive partial transposition criterion, the realignment criterion and the criteria based on the correlation matrices.

11 pages

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• The norms of Bloch vectors and classification of four qudits quantum states
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• Separability discrimination and decomposition of $m$-partite quantum mixed states
• Separability criteria based on Bloch representation of density matrices
• Entanglement Witnesses Based on Symmetric Informationally Complete Measurements
• Entanglement transitivity problems
• Separability criteria based on Heisenberg-Weyl representation of density matrices
• Bounds on Multipartite Concurrence and Tangle
• A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices
• Necessary conditions for classifying m-separability of multipartite entanglements
• Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity
• Detection of entanglement for multipartite quantum states
• Detection power of separability criteria based on a correlation tensor: a case study
• Criteria of genuine multipartite entanglement based on correlation tensors
• On genuine entanglement for tripartite systems
• Robust entanglement measure for mixed quantum states
• Decomposition of completely symmetric states states
• Separability criteria based on the correlation tensor moments for arbitrary dimensional states
• A note on lower bounds of concurrence for arbitrary dimensional bipartite quantum states
• On Sufficient and Necessary Criteria of Multipartite Quantum Entanglement
• Improved tests of genuine entanglement for multiqudits