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Ruling out alternatives to quantum theory: paper in Physical Review Letters

13 September 2011

Physicists can't help but worry they are missing something. The mathematics of quantum theory predicts some hard-to-fathom effects that experimentalists think they've seen, but the differences between what theory can describe and what experimentalists can measure leaves a little room for doubt.

In a new paper, CQT's Esther Hänggi and her collaborators at ETH Zurich in Switzerland take a theoretical approach to tackling this doubt. They show that it may be possible to rule out in principle that results interpreted as quantum could be explained by alternative theories involving faster-than-light communication. The result is published in Physical Review Letters.

Experimentalists have been particularly interested in studying 'non-local' correlations between systems. Non-local means the systems are connected in a way that transcends physical space. Quantum theory makes the distinctive prediction that non-local correlations are instant: for example, a measurement of the polarization of one of a pair of quantum-entangled photons should immediately set the polarization of the other, no matter how far the photons are apart, without either photon's polarization being in any way predetermined. Einstein called this "spooky action at a distance".

Because experiments can only be carried out over finite distances and measurements done with finite speed, they cannot test 'immediately' exactly. Instead, experimental results set a limit on how quickly signals would have needed to travel for one photon to have communicated with the other during the course of the experiment. This limit has already been pushed above light speed, the universal speed limit set by special relativity, but physicists would prefer to rule out the possibility of superluminal but finite-speed 'hidden' communication too.

Considering correlations between three parties, Esther and her collaborators find an example state for which they can rule out theoretically that finite-but-faster-than-light speed communication mediates its non-local correlations.

They imagine three parties Alice, Bob and Charlie, with Alice and Bob and Bob and Charlie sharing non-local correlations transmitted by superluminal communication. They then find an example for which the correlations between A and B and B and C imply non-locality between A and C – a property the researchers describe as "transitive non-local". Transitivity is incompatible with the non-local correlations being transmitted at any finite speed, since the distance between A and C can be greater than that between A and B or B and C. If the communication speed were finite, these shorter distances could be set to equal the maximum distance travelled by the superluminal communication in the measurement time, and then how would the correlations between A and C be explained? The only consistent explanation is that any hidden communication happens at infinite speed – a situation equivalent to quantum theory.

The catch is that the correlated three-party state for which Esther and her coauthors show this property is not a quantum state. They considered non-local correlations in general, and quantum physics represents a special set of such states. The researchers are now searching for a three-party non-local state that is compatible with quantum mechanics. "It's trial and error, and so far only error" says Esther.

There's also the outside chance that quantum states don't have this property of transitivity, that it's something that helps to single out quantum states from the general non-local set. Looking at the general set is an approach to understanding where quantum rules come from. "We are trying to study quantum mechanics from the outside," says Esther.

For more details, see "Non-locality is transitive", Physical Review Letters 107, 100402 (2011); arXiv:1102.5685.

Esther started this work while at ETH Zurich, home to her coauthors on this paper Sandro Coretti and Stefan Wolf. Esther joined CQT as a Research Fellow in the group of Principal Investigator Stephanie Wehner in March 2011.

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