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
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
Geometry of Quantum States: An Introduction to Quantum Entanglement
Geometry of Quantum States: An Introduction to Quantum Entanglement
The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
A matrix realignment method for recognizing entanglement
Quantum Information & Computation
Computational complexity of the quantum separability problem
Quantum Information & Computation
Quantum Information & Computation
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We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.