Proposals for ruling out the real quantum theories in an entanglement-swapping quantum network with causally independent sources

TL;DR

This paper proposes a new method to distinguish real from complex quantum theories using entanglement swapping in causally independent quantum networks, improving discrimination capabilities over previous approaches.

Contribution

It introduces a novel discrimination scheme for real versus complex quantum theories in causally independent networks, employing an optimized correlation function and advanced computational techniques.

Findings

The proposed method enhances the ability to differentiate real and complex quantum theories.

Optimal coefficients for the correlation function improve discrimination power.

The approach extends the study of quantum nonlocality to more complex network scenarios.

Abstract

The question of whether complex numbers play a fundamental role in quantum theory has been debated since the inception of quantum mechanics. Recently, a feasible proposal to differentiate between real and complex quantum theories based on the technique of testing Bell nonlocalities has emerged [Nature 600, 625-629 (2021)]. Based on this method, the real quantum theory has been falsified experimentally in both photonic and superconducting quantum systems [Phys. Rev. Lett. 128, 040402 (2022), Phys. Rev. Lett. 128, 040403 (2022)]. The quantum networks with multiple independent sources which are not causally connected have gained significant interest as they offer new perspective on studying the nonlocalities. The independence of these sources imposes additional constraints on observable covariances and leads to new bounds for classical and quantum correlations. In this study, we examine the discrimination between the real and complex quantum theories with an entanglement swapping scenario under a stronger assumption that the two sources are causally independent, which wasn't made in previous works. Using a revised Navascu\'es-Pironio-Ac\'in method and Bayesian optimization, we find a proposal with optimal coefficients of the correlation function which could give a larger discrimination between the real and quantum theories comparing with the existing proposals. This work opens up avenues for further exploration of the discrimination between real and complex quantum theories within intricate quantum networks featuring causally independent parties.