  Quantum theory demands that, in contrast to classical physics, not all
properties can be simultaneously well defined. The Heisenberg Uncertainty
Principle is a manifestation of this fact. Another important corollary arises
that there can be no joint probability distribution describing the outcomes of
all possible measurements, allowing a quantum system to be classically
understood. We provide the first experimental evidence that even for a single
three-state system, a qutrit, no such classical model can exist that correctly
describes the results of a simple set of pairwise compatible measurements. Not
only is a single qutrit the simplest system in which such a contradiction is
possible, but, even more importantly, the contradiction cannot result from
entanglement, because such a system is indivisible, and it does not even allow
the concept of entanglement between subsystems.
