Bell Inequalities with Communication Assistance

Abstract

In this paper we consider the possible correlations between two parties using local machines and shared randomness with an additional amount of classical communication. This is a continuation of the work initiated by Bacon and Toner in Ref. [\textit{Phys. Rev. Lett.} \textbf{90}, 157904 (2003)] who characterized the correlation polytope for $2\times 2$ measurement settings with binary outcomes plus one bit of communication. Here, we derive a complete set of Bell Inequalities for $3\times 2$ measurement settings and a shared bit of communication. When the communication direction is fixed, nine Bell Inequalities characterize the correlation polytope, whereas when the communication direction is bi-directional, 143 inequalities describe the correlations. We then prove a tight lower bound on the amount of communication needed to simulate all no-signaling correlations for a given number of measurement settings.

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Cited by in corpus (15)

• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• Causal hierarchy of multipartite Bell nonlocality
• Non-classicality of temporal correlations
• Concentration phenomena in the geometry of Bell correlations
• Bell scenarios with communication
• EPR Steering inequalities with Communication Assistance
• Probing the Non-Classicality of Temporal Correlations
• Bell inequalities with one bit of communication
• Robust Bell inequalities from communication complexity
• Neural Network Approach to the Simulation of Entangled States with One Bit of Communication
• The minimal communication cost for simulating entangled qubits
• Multistage games and Bell scenarios with communication
• Explaining quantum correlations through evolution of causal models
• Beating one bit of communication with quantum correlations in smaller dimensions
• Beating one bit of communication with and without quantum pseudo-telepathy