  For a given Hamiltonian $H$ on a multipartite quantum system, one is
interested in finding the energy $E_0$ of its ground state. In the separability
approximation, arising as a natural consequence of measurement in a separable
basis, one looks for the minimal expectation value $\lambda_{\rm
min}^{\otimes}$ of $H$ among all product states. For several concrete model
Hamiltonians, we investigate the difference $\lambda_{\rm min}^{\otimes}-E_0$,
called separability gap, which vanishes if the ground state has a product
structure. In the generic case of a random Hermitian matrix of the Gaussian
orthogonal ensemble, we find explicit bounds for the size of the gap which
depend on the number of subsystems and hold with probability one. This implies
an effective entanglement criterion applicable for any multipartite quantum
system: If an expectation value of a typical observable among a given state is
sufficiently distant from the average value, the state is almost surely
entangled.
