  We study a separability problem suggested by mathematical description of
bipartite quantum systems. We consider Hermitian 2-forms on the tensor product
$H=K\otimes L$, where $K,L$ are finite dimensional complex spaces. Inspired by
quantum mechanical terminology we call such a form separable if it is a convex
combination of hermitian tensor products $(\sigma_p)^*\odot \sigma_p$ of
1-forms $\sigma_p$ on $H$ that are product forms $\sigma_p=\phi_p\otimes
\psi_p$, where $\phi_p\in K^*$, $\psi_p\in L^*$.
  We introduce an integral representation of separable forms. In particular, we
show that the integral of $(D_{z^*}}\Phi)^*\odot D_{z^*}\Phi$ of any square
integrable map $\Phi:\C^n\to \C^m$, with square integrable conjugate derivative
$D_{z^*}\Phi$, is a separable form. Vice versa, any separable form in the
interior of the set of such forms, can be represented in this way. This implies
that any separable mixed state (and only such states) can be either explicitly
represented in the integral form, or it may be arbitrarily well approximated by
such states.
