Structure of quantum and broadcasting nonlocal correlations

The multipartite setting offers much more complexity of nonlocality than the bipartite one. We analyze the structure of tripartite nonlocal correlations by proposing inequalities satisfied by each of type bilocal, broadcasting, and quantum but violated by the other two. One of the inequalities satisfied by broadcasting correlations is generalized for multipartite systems. The study of its quantum mechanical violation reveals that Greenberger-Horne-Zeilinger-like states exhibit new, powerful correlations.

Figure 1

Representation of the overall structure of different bilocal, broadcasting, and quantum correlations. Ddashed lines represent inequalities given by (6), (7), (9), (10), and (13). Here $B$ represents the Bell-CHSH term ($\langle a^0{b}^0\rangle +\langle a^0{b}^1\rangle +\langle a^1{b}^0\rangle -\langle a^1{b}^1\rangle$) [3], which is bounded by $2\sqrt{2}$ in QM.

Figure 2

QM violation of (16) for GHZ-like states, (17).