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 $N\ge 4$. It is shown that $\Phi$ detects many entangled states with a 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.

• Received 3 May 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.080501