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 fact1. 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 results2,3,4,5 imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found6,7,8,9,10 and tested experimentally11,12 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 introduced13 and tested experimentally14,15,16. 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 qutrits17,18 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, Binicioğlu and Shumovsky19. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.
This work was supported by the ERC (Advanced Grant QIT4QAD), the Austrian Science Fund (Grant F4007), the EC (Marie Curie Research Training Network EMALI), the Vienna Doctoral Program on Complex Quantum Systems and the John Templeton Foundation. We acknowledge A. A. Klyachko for discussion of the proposal made in ref. 19; M. Hentschel, M. Kacprowicz and G. J. Pryde for discussions of technical issues; A. Cabello, S. Osnaghi, H. M. Wiseman and M. Z˙ukowski, with whom we discussed the conceptual issues; and M. Nespoli for help during the early stages of the experiment.
The file contains Supplementary Text and Data 1-5, Supplementary Figure 1 with a legend and Supplementary Table 1.