Optimal discrimination between real and complex quantum theories

TL;DR

This paper determines the minimal experimental settings needed to distinguish real quantum theory from complex quantum theory, showing that three settings suffice for certain observers, but fewer settings are inadequate.

Contribution

It refines previous proposals by identifying the minimal number of settings required for testing real versus complex quantum theories under separability assumptions.

Findings

Three settings are sufficient for certain observers to test real quantum theory.

Two settings and two outcomes are insufficient for such tests.

The ratio of maximum violations between complex and real theories is smaller than in previous proposals.

Abstract

We find the minimal number of settings to test quantum theory based on real numbers, assuming separability of the sources, modifying the recent proposal [M.-O. Renou et al., Nature 600, 625 (2021)]. The test needs only three settings for observers $A$ and $C$, but the ratio of complex to real maximum is smaller than in the existing proposal. We also found that two settings and two outcomes for both observes are insufficient.