Reply To: The Quantum Cheshire Cat Experiment of Denkmayr et al

[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