Partial independence suffices to rule out Real Quantum Theory experimentally

TL;DR

This paper demonstrates that partial source independence is enough to rule out Real Quantum Theory in explaining quantum correlations, highlighting the necessity of complex numbers in quantum physics.

Contribution

It introduces a tradeoff between source independence and Bell values in Real Quantum Theory and shows how complex correlations can be simulated with real systems under certain conditions.

Findings

Partial independence suffices to exclude Real Quantum Theory.

A tradeoff between source independence and Bell value is established.

Real quantum systems require specific entanglement to replicate complex quantum correlations.

Abstract

The role of complex quantities in quantum theory has been puzzling physicists since the beginnings. It is thus natural to ask whether, in order to describe our experiments, the mathematical structure of complex Hilbert spaces it is built on is really necessary. Recently, it was shown that this structure is inevitable in network scenarios with independent sources. More precisely, Real Quantum Theory cannot explain the predictions of (Complex) Quantum Theory [Renou et al., Nature 600, 2021]. Here, we revisit the independence assumption underlying this work. We show that assuming partial independence is sufficient for showing the inadequacy of Real Quantum Theory. We derive a tradeoff between source independence and the Bell value achievable in Real Quantum Theory, which also lower bounds the source correlations required to explain previous experiments by means of real quantum systems. We further show that 1 bit of entanglement is necessary and sufficient for recovering the complex quantum correlations by means of Real Quantum Theory in the scenario from [Renou et al., Nature 600, 2021]. Finally, building on [McKague et al., PRL 102, 2009], we provide a construction to simulate any complex quantum setup with m independent sources by means of Real Quantum Theory, by allowing the sources to share a m real-qubit entangled state in the first round of the experiment.