# Bell inequalities with one bit of communication

## TL;DR

This paper explores Bell inequalities in scenarios where two parties with binary outcomes are allowed one bit of classical communication, developing a method to identify facet inequalities and revealing connections to traditional Bell inequalities.

## Contribution

The authors introduce a novel method for finding facet inequalities in Bell scenarios with one bit of communication, including a comprehensive set for a specific three-input case.

## Key findings

- Identified 668 inequivalent facet inequalities for the scenario with three inputs.
- Some inequalities are derived from classical Bell inequalities without communication.
- The method overcomes difficulties in direct facet enumeration.

## Abstract

We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We develop 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 solve 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 the facet inequalities found in scenarios without communication, the well known Bell inequalities.