# Quantum theory based on real numbers cannot be experimentally falsified

**Authors:** Timothée Hoffreumon, Mischa P. Woods  
**arXiv:** [2603.19208](https://arxiv.org/abs/2603.19208)  
**Date:** 2026-03-19  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2603.19208v1/

## Key points

- Real Quantum Theory (RQT) replaces complex amplitudes with real ones while maintaining the standard composition rule
- RQT successfully reproduces single-party and bipartite Bell correlations observed in Quantum Theory (QT)
- Concerns raised about RQT's lack of local tomography and potential divergence in broader local experiments
- Study suggests a bilocal network experiment could disprove RQT without affecting QT, casting doubt on their empirical equivalence
- Analysis challenges previous conclusion by highlighting an untestable assumption underlying the findings
- Product-state independence vs. operational independence distinction crucial for understanding correlation structures in both theories
- Every finite network correlation achievable in QT can also be achieved in RQT under similar measurement locality conditions by imposing operational constraints on source independence
- Empirical indistinguishability of QT and RQT restored, shedding light on their differing interpretations of correlation structures within the same observed world
- Importance of considering operational constraints when evaluating theoretical frameworks in quantum physics

## Summary

In the realm of quantum theory, the question of whether complex numbers are essential for experimental results has long been debated. Real Quantum Theory (RQT) offers an alternative approach by replacing complex amplitudes with real ones while maintaining the standard composition rule. RQT successfully reproduces single-party and bipartite Bell correlations observed in Quantum Theory (QT). However, concerns have been raised about its lack of local tomography and potential divergence in broader local experiments. A study by Renou et al. suggested that a bilocal network experiment could disprove RQT without affecting QT, casting doubt on the empirical equivalence of the two theories. A new analysis challenges this conclusion by highlighting an untestable assumption underlying the previous findings. The distinction between product-state independence and operational independence plays a crucial role in understanding the correlation structures predicted by both theories. By imposing operational constraints on source independence, it is demonstrated that every finite network correlation achievable in QT can also be achieved in RQT under similar measurement locality conditions. This equivalence extends to multipartite protocols involving channels and measurements with specified locality structures, reinforcing the idea that as long as no violations of QT are observed, RQT cannot be experimentally falsified. These results not only restore the empirical indistinguishability of QT and RQT but also shed light on their differing interpretations of correlation structures within the same observed world. The findings challenge previous assumptions about the experimental distinguishability of quantum theories based on real numbers and highlight the importance of considering operational constraints when evaluating theoretical frameworks in quantum physics.