In a classical world, properties of physical systems do not depend on their own measurement, and also not on any other measurements made on the system. In this case, there are joint probability distributions for the system’s properties. In the language of quantum mechanics, such worlds can be described by ‘non-contextual’ hidden-variables models. That in a quantum-mechanical world such joint probability distributions sometimes cannot obtain was established by a series of deep theorems, essentially from Gleason (1957) to Kochen-Specker (1967). It has been previously shown, both in theory and in experiment, that there are simple cases of physical systems, such as pairs of qubits, which behave in accordance to quantum mechanics and thus in conflict with the classical assumption of joint probability distributions.
Theoretical results show that the simplest system (and the simplest set of properties) to exhibit non-classical correlations between some of its properties are single three-state systems (‘qutrits’). In a letter published in a recent issue of Nature (23 June 2011), Lapkiewicz et al. reported on an experiment with exactly such a system, i.e., with photonic qutrits. The result, in accordance with quantum mechanics, shows that these systems cannot be described by a non-contextual theory.
Apart from confirming the theorems mentioned, this result is remarkable because it offers experimental evidence that the characteristic non-classicality of quantum mechanics is not exhausted by non-local Bell correlations between different parts of a composite system, i.e. by entanglement, but already manifests itself for systems “without parts”, as Adan Cabello puts it in his News & Views essay explaining the findings of Lapkiewic et al. Cabello points out that Lapkiewicz et al. show that “Bell experiments, composite systems and entangled states are not enough to provide a complete understanding of the physical principles behind quantum mechanics”, as “quantum correlations exist without them.” This is so because the single three-state photons used in the experiment do not permit entanglement, as they are quantum-mechanical simples.