Topics in matrix analysis
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
A Class of Linear Positive Maps in Matrix Algebras
Open Systems & Information Dynamics
The Bloch-Vector Space for N-Level Systems: the Spherical-Coordinate Point of View
Open Systems & Information Dynamics
On independent permutation separability criteria
Quantum Information & Computation
An introduction to entanglement measures
Quantum Information & Computation
Separability criteria based on the bloch representation of density matrices
Quantum Information & Computation
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We 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 matrizationof tensors. Our criterion applies to arbitrary N-partite quantum states inH = Hd1 × Hd2 ×...×HdN. The criterion can test whether a N-partite state is entangledand can be applied to different partitions of the N-partite system. We provideexamples that show the ability of this criterion to detect entanglement. We show thatthis criterion can detect bound entangled states. We prove a sufficiency condition forseparability of a 3-partite state, straightforwardly generalizable to the case N 3, undercertain condition. We also give a necessary and sufficient condition for separability of aclass of N-qubit states which includes N-qubit PPT states.