  We present a framework for deciding whether a quantum state is separable or
entangled using covariance matrices of locally measurable observables. This
leads to the covariance matrix criterion as a general separability criterion.
We demonstrate that this criterion allows to detect many states where the
familiar criterion of the positivity of the partial transpose fails. It turns
out that a large number of criteria which have been proposed to complement the
positive partial transpose criterion - the computable cross norm or realignment
criterion, the criterion based on local uncertainty relations, criteria derived
from extensions of the realignment map, and others - are in fact a corollary of
the covariance matrix criterion.
