Real- vs complex- valued quantum theories: optimal discrimination based on quantum information

In the present work we find tests of real separability in contrast to complex separability, an alternative to those recently found in Renou et al. "Quantum theory based on real numbers can be experimentally falsified", Nature, 2021. This implies an improved tool for ascertaining, based on the experimental outcome of Bell inequalities, whether quantum physics based solely on the field of real numbers is possible or not.Our proposals require fewer settings for the observers, but the ratio between the complex and real bound is also lower. Also, the numerical check takes a much shorter time.