Quantifying the Nonlocality of Greenberger-Horne-Zeilinger Quantum Correlations by a Bounded Communication Simulation Protocol

The simulation of quantum correlations with finite nonlocal resources, such as classical communication, gives a natural way to quantify their nonlocality. While multipartite nonlocal correlations appear to be useful resources, very little is known on how to simulate multipartite quantum correlations. We present a protocol that reproduces tripartite Greenberger-Horne-Zeilinger correlations with bounded communication: 3 bits in total turn out to be sufficient to simulate all equatorial Von Neumann measurements on the tripartite Greenberger-Horne-Zeilinger state.

Figure 1

Correlation $E_1(\varphi )=E_1({\varphi }_A+{\varphi }_B+{\varphi }_C)$ obtained from Protocol 1, compared to the desired correlation $\cos (\varphi )$.