A Flawed Falsification: Re-examining the Real-Number Quantum Theory Experiment

Renou et al.'s 2021 Nature paper claimed that quantum theory based on real numbers can be experimentally falsified. This post argues otherwise. The paper proposed a test to distinguish between a full quantum gateset using complex numbers and a real-only subset. However, the author demonstrates that a real-only quantum computer, leveraging entanglement, can pass the test. The crucial, hidden assumption is that participating quantum computers begin without entanglement—a detail buried in the supplementary materials, severely undermining the experiment's validity.