Recurrent construction of optimal entanglement witnesses for 2N-qubit systems

We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space corresponding to 2N qubits (N qubits in each subsystem). Our construction provides a method of generalization of the Robertson map that naturally meshes with 2N-qubit systems, i.e., its structure respects the 2(2N) growth of the state space. We prove that for N > 1 these witnesses are indecomposable and optimal. As a byproduct we provide a family of PPT (Positive Partial Transpose) entangled states.