Experimental Test of Contextuality Based on State Discrimination with a Single Qubit

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 ^171Yb^+ 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.