Topics in matrix analysis
Quantum computation and quantum information
Quantum computation and quantum information
Classical deterministic complexity of Edmonds' Problem and quantum entanglement
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Further Results on the Cross Norm Criterion for Separability
Quantum Information Processing
A matrix realignment method for recognizing entanglement
Quantum Information & Computation
An introduction to entanglement measures
Quantum Information & Computation
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Exploiting the cone structure of the set of unnormalized mixed quantum states, we offer an approach to detect separability independently of the dimensions of the subsystems. We show that any mixed quantum state can be decomposed as 驴 = (1驴驴)C 驴 + 驴E 驴 , where C 驴 is a separable matrix whose rank equals that of 驴 and the rank of E 驴 is strictly lower than that of 驴. With the simple choice $${C_{\rho}=M_{1}\otimes M_{2}}$$ we have a necessary condition of separability in terms of 驴, which is also sufficient if the rank of E 驴 equals 1. We give a first extension of this result to detect genuine entanglement in multipartite states and show a natural connection between the multipartite separability problem and the classification of pure states under stochastic local operations and classical communication. We argue that this approach is not exhausted with the first simple choices included herein.