Optimal discrimination between real and complex quantum theories

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.

7 pages, 4 figures, MATLAB script in anciliary files

References in corpus (5)

• Quantum theory based on real numbers can be experimentally falsified
• Testing real quantum theory in an optical quantum network
• Ruling out real-valued standard formalism of quantum theory
• Simulating quantum systems using real Hilbert spaces
• Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities

Cited by in corpus (1)

• Resource Theory of Imaginarity: New Distributed Scenarios