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-toreal bound on a Bell-type parameter. In contrast to previous theoretical and experimental proposals the test requires three settings for the parties A and C, but also six settings for the middle party B, assuming separability of the sources. The bound we found for this symmetric configuration imposed on a real theory is 14.69 while the complex maximum is 18. This large theoretical difference enables us to demonstrate the concomitant experimenvia a designed quantum network, without resorting to error mitigation, obtaining as a result 15.44 at more than 100 standard deviations above the found real bound.