Abstract
We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We developed a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult. Using this method, we partially solved the scenario where Alice and Bob choose between three inputs, finding a total of 668 inequivalent facet inequalities (with respect to relabelings of inputs and outputs). We also show that some of these inequalities are constructed from facet inequalities found in scenarios without communication, that is, the well-known Bell inequalities.
Highlights
Bell nonlocality [1,2] is one of the most intriguing phenomena encountered in modern physics
We present a method and notation to find facets of Bell scenarios supplemented by one bit of classical communication
+ 1 scenario, we found no quantum violation of the one-bit bound
Summary
Bell nonlocality [1,2] is one of the most intriguing phenomena encountered in modern physics. One can ask how many bits of information are needed to reproduce correlations arising from projective measurements on any two-qubit state [6,8,9,11]. It is interesting that such a well-posed binary-answer question for projective measurements on two-qubit pure states has still not been answered, even though several authors have worked on this problem [13,14]. This illustrates the technical difficulty of studying nonlocality. We do not provide an answer to Toner and Bacon’s question here, our results already provide a deeper understanding of Bell-like inequalities for scenarios with one bit of communication. We conclude by discussing the general structure of Bell-like inequalities with one bit of communication, and future directions of research
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