  Exploring quantum phenomena beyond predictions of any classical model has
fundamental importance to understand the boundary of classical and quantum
descriptions of nature. As a typical property that a quantum system behaves
distinctively from a classical counterpart, contextuality has been studied
extensively and verified experimentally in systems composed of at least three
levels (qutrit). Here we extend the scope of experimental test of contextuality
to a minimal quantum system of only two states (qubit) by implementing the
minimum error state discrimination on a single $^{171}$Yb$^+$ ion. We observe a
substantial violation of a no-go inequality derived by assuming
non-contextuality, and firmly conclude that the measured results of state
discrimination cannot be reconciled with any non-contextual description. We
also quantify the contextual advantage of state discrimination and the
tolerance against quantum noises.
