The Quantum Cheshire Cat Experiment of Denkmayr et al

[Mark Stuckey]

In a July 2014 Nature Communications paper, Denkmayr et al. made the spectacular claim that in their interferometer experiment “the neutron and its spin are spatially separated.” They support their claim via their so-called “weak values” in this experiment, thus they claim to have successfully carried out the quantum Cheshire Cat experiment. In the short synopsis of http://arxiv.org/abs/1410.1522 attached here, we show that the authors’ own theory and experimental outcomes, along with the quantum mechanical explanation of the weak values in this experiment, combine unambiguously to refute their spectacular claim. While they measured the correct weak values for the quantum Cheshire Cat experiment, those weak values were measured with a quadratic, instead of the required linear, magnetic field Bz interaction. The quadratic Bz interaction means there will be empirical evidence for a spin z coupling on both paths of the interferometer, no matter how weak you make Bz, and this destroys the quantum Cheshire Cat effect.

[Miroljub Dugic]

Hi Mark,

do you have any comments on this: http://arxiv.org/abs/1409.0808 ?

Best regards,

Miroljub

[Mark Stuckey]

I’ve had extensive contact with Raul Correa since last fall about his paper and ours. He failed to tell me that he got his paper accepted in New J Phys, but he apologized this week 🙂

Correa et al explain how Aharonov’s proposed quantum Cheshire Cat (qCC) experiment with photons can be understood via interference. When they discuss the Denkmayr et al alleged qCC experiment with neutrons, Correa points out that Denkmayr’s so-called “qualitative result” is easily explicable via interference. We point out that Denkmayr’s “qualitative result” is not used to obtain their weak values and does not establish qCC, regardless of how you might explain it. As Correa wrote to me, “And surely you point different things. We don’t address the inconsistencies in their arguments, like the diminished counts even when the field is on the arm that has ‘no spin’. And of course the very interesting remark that the quadratic term of the Bz interaction is connected to the “where the neutron is” weak value, and hence means they can’t look for the Cheshire Cat with this interaction — very clever indeed!”

To link Correa’s explanation of Aharonov’s original qCC proposal with photons to our work showing how Denkmayr failed to instantiate qCC with neutrons, you need to look at how Correa obtains the photon amplitude for the qCC experiment, i.e., the approximate photon amplitude at detector D1 when the transverse pointer displacements are much smaller than the beam width (a weak measurement). That approximate amplitude (his Eq 7) is obtained via expanding the exact photon amplitude (his Eq 5) to first order (linear terms). If you keep second order (quadratic terms) in the expansion of the exact amplitude, you won’t get the proper form for the qCC amplitude. Correa points out that this is also key in Danan et al’s experiment, “Asking photons where they have been.” A first-order (linear) interaction is crucial for doing a weak measurement.

So, what we point out in our paper is that Denkmayr et al have a quadratic Bz interaction that cannot be avoided in their experimental approach with neutrons. It is this quadratic term that gives rise to a 3% decrease in the neutron intensity at detector O when Bz is in path II, which is just as pronounced as the 3% increase in the neutron intensity at detector O when Bz is in path I (that increase is due to the linear term in the Bz interaction). Thus, you can never make Bz weak enough to get rid of the effect in path II without also getting rid of the effect in path I (where you need to have it). Bottom line: it’s impossible to get the qCC effect with this experimental set-up.

Hope that answers your question, Miroljub!

Thanks for asking,
Mark

[Miroljub Dugic]

Hi Mark,

Thanks a lot. Good point(s)!

Best,
Miroljub

[Mark Stuckey]

Raul told me today that he doesn’t see any connection between Aharonov qCC and Denkmayr (alleged) qCC because Denkmayr doesn’t have a displaced pointer state. A weak values theorist (who asked not to be cited) agreed with our analysis saying “weakly enough” in Denkmayr should have read “linearly” because weak measurement requires linear interaction. Therefore, he said the quadratic interaction of Denkmayr “would seem fatal.” That’s why I think the parallel between Aharonov qCC and Denkmayr qCC would be, as I stated above, Correa’s Eq 5 giving his Eq 7.

This is an interesting issue for weak values in general, because in Denkmayr <SzP1> = 1, <P1> = 0, <SzP2> = 0, and <P2> = 1. If the Bz interaction had been linear, these “observables” would account directly for a reduction in the intensity at detector O (Io) for the absorber in path 2 <P2> = 1, but no change in Io for the absorber in path 1 <P1> = 0. And, there would have been an increase in Io for Bz in path 1 <SzP1> = 1, but no change in Io for Bz in path 2 <SzP2> = 0. As it turns out, the quadratic Bz interaction leads to a decrease in Io for Bz in path 2, which is accounted for by <P2> = 1. This is where we claim qCC is violated, it’s what Correa refers to when he writes, “the quadratic term of the Bz interaction is connected to the ‘where the neutron is’ weak value [<P2> = 1], and hence means they can’t look for the Cheshire Cat with this interaction.” However, these “observables” are used properly to account for what they *did* observe. Stephan Sponar (experimentalist on Denkmayr et al) attended my presentation in Vaxjo two weeks ago and said he understood those four “observables” entailed qCC. But, if that were true, you would have two very different empirical results associated with qCC, one of which makes sense (linear Bz interaction) and one of which doesn’t (quadratic Bz interaction). So, in our paper, we have a section where we explain what <SzP1> = 1, <P1> = 0, <SzP2> = 0, and <P2> = 1 mean in Denkmayr.

Thus, while Denkmayr doesn’t give us qCC, it does show us empirically that weak value “observables” have different meanings in different weak scenarios, which is interesting. I would like to hear from more of the weak values community on this issue.

[Mark Stuckey]

The arXiv paper has been rewritten in the form it was just today submitted to New J Phys (where Aharonov published his quantum Cheshire Cat proposal and Correa et al. published their qCC paper). Yesterday, Nature Comm said they would not publish our Brief Communication Arising on the refutation because it’s based on an unpublished technical point (and so could not be conveyed in the 600-word limit of a BCA). Rather, they advised us to seek publication elsewhere of the full 15-page explanation of our claim — linear interaction is required to make the qCC inference from the weak values, i.e., quadratic interaction kills qCC. Here again is the link to the arXiv paper http://arxiv.org/abs/1410.1522

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