Experimental non-classicality of an indivisible quantum system

Photonic qutrits beyond the classical world Quantum theory requires that, in contrast to classical physics, not all properties can be simultaneously well defined. Entanglement between the subsystems of a composite physical system is often considered to be the reason, although theory suggests that there is a deeper incompatibility between quantum mechanics and classical physics. Lapkiewicz et al . report an experiment with single three-state systems (photonic qutrits) that vividly demonstrates this incompatibility. They show that classical theory cannot explain the results, even though a qutrit is indivisible and cannot support entanglement between subsystems. 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 , 3 , 4 , 5 imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found 6 , 7 , 8 , 9 , 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 , 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 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, Binicioğlu and Shumovsky 19 . Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.