Quantum Advantages of Communication Complexity from Bell Nonlocality

Communication games are crucial tools for investigating the limitations of physical theories. The communication complexity (CC) problem is a typical example, which several distributed parties attempt to jointly calculate given function with limited classical communications. In this work, we present method construct CC problems from Bell tests in graph-theoretic way. Starting an experimental compatibility graph and corresponding test function, target that encodes information each edge can be constructed; then, using by pre-sharing entangled states, its success probability exceeds arbitrary strategy. non-signaling protocol based on Popescu–Rohrlich box also discussed, case reaches one.