  A general formulation of the problem of detection for a pair of two cones is
presented. The special case is the detection of entangled states by
entanglement witnesses. Having defined what means "to detect", one can identify
the subset of elements, which detect optimally. I will present the properties
of this set for a general pair of cones.
  In particular, I prove the generalization of the theorem of Lewenstein,
Krauss, Cirac, Horodecki. The entanglement witness $W$ is optimall if the set
of product vectors $\{\phi \otimes \psi: \langle \phi \otimes \psi | W | \phi
\otimes \psi \rangle = 0\}$ spans the whole Hilbert space of a system. There
exist optimall entangled witness, which do not fullfill this property. It is
closely related to some geometrical properties of the boundary of the set of
entanglement witnesses and it is possible to say something more about location
of such extraordinary states.
