Covariance matrices and the separability problem

We propose a unified approach to the separability problem which uses a representation of a quantum state by a covariance matrix of suitable observables. From the practical point of view, our approach leads to entanglement criteria that allow to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental point of view, our approach leads to insights into the relations between several known entanglement criteria as well as their limitations