Separability criteria based on the Bloch representation of density matrices

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.Comment: 17 pages, no figures; Section 4.2 improved; final version: minor changes, added references, to appear in QI

Separability conditions from the Landau-Pollak uncertainty relation

We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested, and compared with previously stated criteria, by applying them to states whose separability limits are already known. Our results are also extended to multipartite and higher-dimensional systems.Comment: 20 page