Experimental non-classicality of an indivisible quantum system

In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact(1). Alternatives have been explored-notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results(2-5) imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found(6-10) and tested experimentally(11,12) with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced(13) and tested experimentally(14-16). A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits(17,18) which provides evidence that no joint probability distribution describing the outcomes of all possible measurements-and, therefore, no non-contextual theory-can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioglu and Shumovsky(19). Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.