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I work as a theorist with my current research interests in "quantum contextuality". For those perusing the question, this is essentially a generalization of non-locality where we can show a quantum system does not admit a hidden-variable model. So in some sense, it's impossible to look at the problem classically.

For further background, contextuality can often be formulated as a resource for quantum computation-- which is the reason why we're interested in it. Our talking points to people are that contextuality is the right way of characterizing what's essentially quantum about a system (many would debate us on that, but that's perhaps for another thread).

What I've found so far is a proposed experiment for testing contextuality: Cabello-2016-Experiment and a description of the implications of a successful contextuality experiment: Winter-2014-Implications.

Most experimentalists tend to focus on entanglement (understandably; it's a lot easier to measure and more concrete to think about) - but are there any experimental groups currently working on contextuality experiments?

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    $\begingroup$ Might be relevant also PhysRev A paper. People in queens from that paper I believe have ties to experiments but whether specifically on contextuality experiments I don't know. $\endgroup$ – snulty Mar 15 '18 at 0:42
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    $\begingroup$ Curiosity, but is "quantum contextuality" generally held to be a uniquely quantum phenomena, or is it meant as an analog to some sort of non-quantum contextuality? $\endgroup$ – Nat Mar 15 '18 at 0:50
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    $\begingroup$ I wanted to clarify that I'm interested in contextuality as it applies to quantum systems, however, some classical systems have been known to exhibit contextuality, e.g. arXiv:1310.4990. In general resource-wise, we are interested in state-dependent contextuality, for which I don't think classical systems exhibit. $\endgroup$ – Emily Tyhurst Mar 15 '18 at 2:57
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The Quantum Reality group at the Centre for Quantum Technologies (National University of Singapore) https://qreality.quantumlah.org/

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