On m = N/2 Dicke states as maximally entangled pure states

Abstract

We show that the m = N/2 subset of the Dicke states could be chosen to define an N-qubit maximally entangled pure state since it retains the properties of both the GHZ and W states which make these two states main canditate for maximally entangled pure states of different entanglement measures. On the one hand, it retains the “genuineness” property of a GHZ state where tracing out all the subsystems leaves a qubit which is maximally mixed. On the other hand, it also has the “robustness” property of a W state whereby tracing out all but two qubits leaves a state which is still bipartite entangled.