Multipartite monogamous relations for entanglement and discord

The distribution of quantum correlations in multipartite systems plays a significant role in several aspects of quantum information theory. While it is well known that these quantum correlations cannot be freely distributed, the way that they are shared in a multipartite system is an open problem even for a small set of qubits. Based on monogamylike relations between entanglement and discord for $n$-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary multipartite pure states.

Figure 1

(a) The inaccessible information of part 1, given an observation on the rest, with the exception of that immediately on its left, i.e., part $n$. (b) The inaccessible information on part 1, but now given an observation on the rest, with the exception of that immediately on its right, i.e., part 2. The monogamous equality is reached doing the same procedure for all $n$ parts.