  Our common understanding of the physical world deeply relies on the notion
that events are ordered with respect to some time parameter, with past events
serving as causes for future ones. Nonetheless, it was recently found that it
is possible to formulate quantum mechanics without any reference to a global
time or causal structure. The resulting framework includes new kinds of quantum
resources that allow performing tasks - in particular, the violation of causal
inequalities - which are impossible for events ordered according to a global
causal order. However, no physical implementation of such resources is known.
Here we show that a recently demonstrated resource for quantum computation -
the quantum switch - is a genuine example of "indefinite causal order". We do
this by introducing a new tool - the causal witness - which can detect the
causal nonseparability of any quantum resource that is incompatible with a
definite causal order. We show however that the quantum switch does not violate
any causal nequality.
