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We provide a recurrent construction of entanglement witnesses for a bipartitesystems living in a Hilbert space corresponding to $2N$ qubits ($N$ qubits ineach subsystem). Our construction provides a new method of generalization ofthe Robertson map that naturally meshes with $2N$ qubit systems, i.e., itsstructure 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 providea new family of PPT (Positive Partial Transpose) entangled states.

Recurrent construction of optimal entanglement witnesses for 2N qubit systems