Actually, you can't test if quantum uses complex numbers

A detailed critique of a 2021 Nature paper claiming that quantum mechanics requires complex numbers and can be experimentally tested. The author demonstrates that the paper's test can be spoofed using real-only quantum computers by distributing entangled phase gradient states before testing begins. The critique reveals that the original paper's proof relies on an unstated assumption that players cannot pre-share entangled states, which is buried in supplementary materials rather than clearly disclosed in the main text.