  We report an experimental certification of indefinite causal order that
relies only on the characterization of the operations of a single party. We do
so in the semi-device-independent scenario with the fewest possible assumptions
of characterization of the parties' local operations in which indefinite causal
order can be demonstrated with the quantum switch. To achieve this result, we
introduce the concept of semi-device-independent causal inequalities and show
that the correlations generated in a photonic quantum switch, in which all
parties are able to collect local outcome statistics, achieve a violation of
this inequality of 224 standard deviations. This result consists of the
experimental demonstration of indefinite causal order with the fewest
device-characterization assumptions to date.
