Optimal Entanglement Criterion for Mixed Quantum States

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Φ which operates on state spaces with even dimension N≥4. It is shown that Φ 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 Φ yields a systematic method for the explicit construction of high-dimensional manifolds of bound entangled states.