I must admit, I have never been tempted to delve deeply into the theory of superconductors. So when I came across a review article by J Q You and Franco Nori entitled “Atomic physics and quantum optics using superconducting circuits”, published in Nature on 30 June 2011, I was about to skip it. But then I discovered the box on page 595 which discusses tests of quantum mechanics based on macroscopic superconducting circuits and realized that this box at least deserves mention in this ongoing series on recent advances in measurements of quantum systems with implications for the foundations of quantum mechanics.
The box discusses three types of tests of quantum mechanics: Bell inequality, Leggett-Garg inequality, and Kochen-Specker theorem. While I disagree with some of the foundational gloss the authors give on these results (for instance, we get the usual spiel about hidden variables in introducing Bell’s theorem), the experiments they list testify to what a resource superconductors can be in foundations. There are no surprises, as all experiments listed confirm quantum mechanics.
Concerning the first topic, Bell’s theorem, the authors mention that a number of experiments using superconducting circuits have been proposed–and at least one of them has been performed. Two points of interest. First, despite the fact that these superconducting circuits are macroscopic they exhibit quantum behaviour, as they violate Bell’s inequality. Second, two studies have been published in 2010 which use Greenberger-Horne-Zeilinger states and thus don’t need to rely on statistics, but get the violation of a Bell-type inequality from a single run.
The second kind of tests are of the Leggett-Garg inequality, which is a kind of temporal analogue of Bell’s inequality. The violation of this inequality has also been shown experimentally (also in 2010!), using Copper pairs as the quantum two-level system.
Regarding the third type of quantum-mechanical tests, of the Kochen-Specker theorem, which prohibits non-contextual hidden-variables theories, only proposals have been made so far; no actual tests have been performed. If successful, the proposed experiment would be quite remarkable: it would confirm–again–macroscopic non-classical behaviour!