Efficient discrimination between real and complex quantum theories

We improve the test to show the impossibility of a quantum theory based on real numbers by a larger ratio of complex-to-real bound on a Bell-type parameter. In contrast to previous theoretical and experimental proposals the test requires three setting for the parties A and C, but also six settings for the middle party B, assuming separability of the sources. The bound for this symmetric configuration imposed on a real theory is 14. 88 whilst the complex maximum is 18. This large theoretical difference enables us to demonstrate the concomitant experimental violation on IBM quantum computer via a designed quantum network, obtaining as a result 15. 44 at more than 80 standard deviations above the real bound.