Just curious what folks think will be the ramifications of this latest finding from the time-symmetric quantum mechanics folks (Tollaksen, Aharonov, etc)

"The pigeonhole principle: "If you put three pigeons in two pigeonholes at least two of the pigeons end up in the same hole" is an obvious yet fundamental principle of Nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed. "

Well, first, I take the "pigeon hole principle" to be a statement in mathematics, not physics, so this argument simply doesn't apply. Second, as far as the physics of actual holes is concerned the fact that the "pigeons" cannot be considered solely as "particles". Or perhaps better wording would be "in so far as we consider the pigeons to be particles, the argument is incorrect and in so far as we don't consider the pigeons to be particles, the argument doesn't apply".

The name "Cheshire Cat" is a metaphor by reference to the smile of the cat from Alice in Wonderland, which smile could be observed independently of the cat.

My analysis of the quantum Cheshire Cat experiment is at http://arxiv.org/abs/1410.1522
This paper is under review at Am. J. Phys. and there is an associated (600-word) Brief Communication Arising under consideration at Nature Communications. Both papers are the result of conversations with colleagues and many exchanges with Denkmayr et al.

I have an analysis of the quantum pigeonhole principle that I'm running by colleagues now. After they weigh in, I will let you know what we think.

Ruta, would you agree quite generally that "weak values" should not be taken very seriously as actual values associated with single systems (not ensembles)?

I personally find the logic a bit tortured and fail to see why such a complex construction should be called a violation of an obviously true principle.

The basic statement is that given three particles placed arbitrarily into two possible boxes, at last two particles must be in the same box. This is obviously true in quantum mechanics. For example, let ## P_{\geq 2} ## denote the projector onto the space of states which have at least two particles in L or R. It is immediate that ##P_{\geq 2} |\psi \rangle =|\psi \rangle ## for any three particle state. Thus I would say the pigeon hole principle is trivially satisfied (every three particle basis state satisfies it) as it must be. In other words, if at any time we make a measurement ##\{P_{\geq 2}, 1- P_{\geq 2}\}## we will always get the first outcome if the system has three particles and only two boxes.

Having not read the remainder of the paper in any detail, let me just assume that the interference experiment, etc. are analyzed correctly. I still don't see what this has to do with violating the pigeonhole principle nor am I convinced that it represents a major new insight into the structure of quantum correlations. I hate to be so negative, but I just currently don't see the point.

Your argument based on projections assumes a standard projective measurement. But weak measurement is not a projective measurement. With weak measurement, it may be the case that if you look at L box you find 1 particle in L box. Likewise, if you look at R box you find 1 particle in R box. Of course, you can always say that there are 2 particles in the other box which you didn't look at, and hence avoid the paradox. (And weak measurement does not allow you to look at both boxes at once.) But how do particles know that you look at one box and not the other? They do, because QM is contextual. Indeed, the strange character of weak measurements seems to be nothing but a manifestation of quantum contextuality: http://lanl.arxiv.org/abs/1409.1535 (the author is the same person as the first author of the now famous PBR theorem)

But some physicists do not really accept contextuality, and for them the results of weak measurements look totally paradoxical. In particular, they tend to think that particles can not know that you look at one box and not the other, so for them it looks as if in each box there is only 1 particle.

Why don't some physicists accept contextuality? All biologists :) do (it's common sense), so that biological and quantum pigeons both obey the pigeonhole principle.

In classical physics, you can measure an object without significantly influencing it. The intuition of physicists is most developed by their experience with classical physics, so I guess it's hard for them to abandon such intuition. Especially when violation of Bell inequalities implies that such a strong influence, if exists, in some cases must also be non-local.

Demystifier, thanks for your response. However, I still fail to see why we have to exhibit all these complications to talk about something simple like the pigeon hole principle.

Of course a projective measurement is not a weak measurement; my claim is that if, in addition to everything else, we make a projective measurement of ## P_{\geq 2} ## at any point in the evolution, we will find yes or 1 with certainty. This is a trivial statement, but shouldn't we identify this trivial statement with the pigeonhole principle?

I maintain the results of the calculation/experiment are not confusing or paradoxical and that what one should call the pigeon hole principle is trivially satisfied. Let me put it this way: the wavefunction of the system + apparatus + environment is a unitarily evolving state ##\rho_{SAE} ## with the property that ##\text{tr}(P_{\geq 2} \rho_S) =1 ## for all time.

Because otherwise no one will make a thread about it :) But maybe they have a clear formulation of a purely quantum effect like Bell's theorem or GHZ? If they do, it doesn't seem like it, because at the end they say "It is still very early to say what the implications of this revision are, but we feel one should expect them to be major since we are dealing with such fundamental concepts."
Incidentally, what do people think about this classical weak value analogy? http://physicsworld.com/cws/article/news/2014/oct/09/are-weak-values-quantum-after-all http://arxiv.org/abs/1403.2362