  Contextuality is a fundamental non-classical property of quantum theory,
which has recently been proven to be a key resource for achieving quantum
speed-ups in some leading models of quantum computation. However, which of the
forms of contextuality, and how much thereof, are required to obtain a speed-up
in an arbitrary model of quantum computation remains unclear. In this paper, we
show that the relation between contextuality and a compuational advantage is
more complicated than previously thought. We achieve this by proving that
generalized contextuality is present even within the simplest subset of quantum
operations, the so-called single-qubit stabilizer theory, which offers no
computational advantage and was previously believed to be completely
non-contextual. However, the contextuality of the single-qubit stabilizer
theory can be confined to transformations. Therefore our result also
demonstrates that the commonly considered prepare-and-measure scenarios (which
ignore transformations) do not fully capture the contextuality of quantum
theory.
