  We develop a strong and computationally simple entanglement criterion. The
criterion is based on an elementary positive map Phi which operates on state
spaces with even dimension N >= 4. It is shown that Phi detects many entangled
states with positive partial transposition (PPT) and that it leads to a class
of optimal entanglement witnesses. This implies that there are no other
witnesses which can detect more entangled PPT states. The map Phi yields a
systematic method for the explicit construction of high-dimensional manifolds
of bound entangled states.
