Efficient discrimination between real and complex quantum theories

TL;DR

This paper presents an improved Bell-type test that distinguishes real from complex quantum theories, demonstrating the violation of the real theory bound on IBM quantum computers with high statistical significance.

Contribution

It introduces a new Bell-type inequality requiring specific measurement settings, with a larger gap between real and complex quantum bounds, enabling experimental discrimination.

Findings

The real quantum theory bound is 14.69, while the complex maximum is 18.

Experimental violation achieved with a value of 15.44 on IBM quantum computers.

Violation is statistically significant at more than 100 standard deviations.

Abstract

We improve the test to show the impossibility of a quantum theory based on real numbers by a larger ratio of complex-to-real bound on a Bell-type parameter. In contrast to previous theoretical and experimental proposals the test requires three settings for the parties $A$ and $C$, but also six settings for the middle party $B$, assuming separability of the sources. The bound we found for this symmetric configuration imposed on a real theory is $14.69$ while the complex maximum is $18$. This large theoretical difference enables us to demonstrate the concomitant experimental violation on IBM quantum computer via a designed quantum network, without resorting to error mitigation, obtaining as a result $15.44$ at more than $100$ standard deviations above the found real bound.