Experimental non-classicality of an indivisible system

In Quantum Mechanics (QM) not all properties can be simultaneously well defined. An important question is whether a joint probability distribution can describe the outcomes of all possible measurements, allowing a quantum system to be mimicked by classical means. Klyachko et al. [PRL 101, 020403 (2008)] derived an inequality which allowed us to answer this question experimentally. The inequality involves only five measurements and QM predicts its violation for single spin-1 particles. This is the simplest system where such a contradiction is possible. It is also indivisible and as such cannot contain entanglement. In our experiment with single photons distributed among three modes (isomorphic to stationary spin-1 particles) we obtained a value of -3.893(9), which lies more than 90 standard deviations below the ``classical'' bound of -3.