Concurrence of Superpositions

Recently, Linden, Popescu and Smolin [Phys. Rev. Lett., 97, 100502 (2006)] have raised the following problem: Given a bipartite quantum state and a certain decomposition of it as a superposition of two others, what is the relation between the entanglement of the state and those of the two states in the superposition? In this paper we use the concurrence vector as a measure of entanglement and investigate upper and lower bounds on the concurrence of the state as a function of the concurrence of the superposed states. We show that the concurrence vector enables us to extend the results to the superpositions of two multipartite states.