Correlation Complementarity Yields Bell Monogamy Relations

We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum nonlocality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on the amount of violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.

Figure 1

The nodes of these graphs represent observers trying to violate Bell inequalities which are denoted by colored edges. (a) The simplest case: two subsets of three parties try to violate CHSH inequality. (b) Four three-party subsets of four parties try to violate Mermin inequality. (c) Two subsets of odd number of parties try to violate multipartite Bell inequality in a scenario in which only one particle is common to two Bell experiments. (d) A binary tree configuration leads to strong monogamy relation.