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.
Taking up Spacetime 
I know very little QM as my specialty is on the field of classical dynamics and the philosophy of space and time.
However, I find the paper you mentioned far from convincing. I will not elaborate here because I agree with this author:
http://www.science20.com/alpha_meme/no_entanglement_no_classicality_or_no_news-80342
Thanks
Thanks for pointing out Vongehr’s reaction to this article, he raises a few important points. Let us agree not to quibble over what ‘classicality’ means. Vongehr may be using a somewhat unusual notion of ‘classicality’, though I am not sure about this. And he admits that the experiment is at odds with non-contextual hidden-variables theories, which is a central claim of the authors. Of course, in a sense, this really is not big news. We knew that these models were under severe pressure since the deep theoretical results in quantum mechanics I mention in the post. But he does seem to get some things wrong: Bell’s theorem is not a disproof of hidden-variables theories; rather, it shows (together with its experimental confirmation, of course) that Nature demands that any adequate theory must be non-local, in one way or another. I know that often people are confused about this point, but the fact that Bohm’s theory evades the scriptures of Bell’s theorem should give them pause. Also, there is a clear conceptual difference between superposition and entanglement, and it is clear that with single photons as used in the experiment, no entanglement is possible.
So what the authors of the article claim seems to stand, with the possible exception of whether they have shown a violation of ‘classicality’. And here, it seems to me that to say that classicality is violated when non-contextuality must be given up is at least not a crazy use of this term. So even though the experiment doesn’t really show anything that theoreticians didn’t know in 1967, the publication in Nature seems justified for exactly the reasons the authors claim.