Monogamy of measurement-induced nonlocality

Measurement-induced nonlocality was introduced by Luo and Fu (2011 Phys. Rev. Lett. 106 120401) as a measure of nonlocality in a bipartite state. In this paper, we will discuss the monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ- and W-states satisfy monogamy relations in the three-qubit case; however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In the case of the four-qubit system, monogamy holds for most of the states in the generic class. The four-qubit GHZ-state does not satisfy the monogamy relation, but the W-state does. We provide several numerical results including counterexamples regarding the monogamy nature of measurement-induced nonlocality. We will also extend our results of the generalized W-class to n-qubit systems. (paper)