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Abstract

Entanglement witnesses have a rich geometrical structure and their construction is a consequence of the Hahn-Banach theorem. These entanglement witnesses are also very useful when detecting multipartite entangled states where one would like to avoid full quantum state tomography which could be very costly.
On other hand, concurrence is one of well-known measure of entanglement for bipartite and multipartite quantum states. In this talk, I establish a relation between concurrence and entanglement witnesses. In particular, I construct entanglement witnesses for three-qubit W and GHZ states in terms of concurrence. I also generalize this construction for multi-qubit states.