# Geometry of the set of synchronous quantum correlations

## TL;DR

This paper offers a comprehensive geometric analysis of the set of synchronous quantum correlations in a specific scenario, demonstrating its closure and bounded Hilbert space dimension for realizations.

## Contribution

It provides the first complete geometric characterization of these correlations and establishes a uniform bound on the Hilbert space dimension needed for their realization.

## Key findings

- The set of synchronous quantum correlations is closed.
- All correlations in this set can be realized with Hilbert space dimension ≤ 16.
- The paper offers a detailed geometric description of these correlations.

## Abstract

We provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario. We show that these correlations form a closed set. Moreover, every correlation in this set can be realized using projection valued measures on a Hilbert space of dimension no more than 16.