Constructing optimal entanglement witnesses. II. Witnessing entanglement in 4N×4N systems

We provide a class of optimal nondecomposable entanglement witnesses for 4N×4N composite quantum systems or, equivalently, another construction of nondecomposable positive maps in the algebra of 4N×4N complex matrices. This construction provides natural generalization of the Robertson map. It is shown that their structural physical approximations give rise to entanglement breaking channels.