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

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

Justyna P. Zwolak and Dariusz Chruściński

Phys. Rev. A 89, 052314 – Published 12 May 2014

Abstract

We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space corresponding to $2 N$ qubits ( $N$ qubits in each subsystem). Our construction provides a method of generalization of the Robertson map that naturally meshes with $2 N$ -qubit systems, i.e., its structure respects the $2^{2 N}$ 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.