  We experimentally observed state-independent violations of Kochen-Specker
inequalities for the simplest indivisible quantum system manifesting quantum
contextuality, a three-level (qutrit) system. We performed the experiment with
a single trapped ^{171}Yb^{+} ion, by mapping three ground states of the
^{171}Yb^{+} ion to a qutrit system and carrying out quantum operatations by
applying microwaves resonant to the qutrit transition frequencies. Our results
are free from the detection loophole and cannot be explained by the
non-contextual hidden variable models.
