  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.
