  Universal contextuality is the leading notion of non-classicality even for
single systems, showing its advantage as a more general quantum correlation
than Bell non-locality, as well as preparation contextuality. However, a
loophole-free experimental demonstration of universal contextuality at least
requires that both operational inequivalence and compatibility loopholes are
closed, which have never been simultaneously achieved to date. In our work, we
experimentally test universal contextuality through (3,3) and (4,3)
communication games, simultaneously restoring operational equivalence and
circumventing the compatibility loophole. Our result exhibits the violation of
universal non-contextuality bound by 97 standard deviations in (3,3) scenario,
and 107 deviations in (4,3) scenario. Notably there are states which exhibit
locality but reveal universal contextuality in both two scenarios. In addition,
our result shows that universal contextuality is more general than preparation
contextuality in (3,3) scenario, while equivalent to preparation contextuality
in (4,3) scenario.
