Quantum Pigeonhole Effect: New Implications for Correlations

[dm4b]

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

http://physicsworld.com/cws/article...ical-pigeons-are-the-latest-quantum-conundrum

Now, Jeff Tollaksen of Chapman University in California and colleagues in Israel, Italy and the UK have proposed an equally bizarre scenario dubbed the "quantum-pigeonhole effect". The paradox begins with the observation that when you put three pigeons in two pigeonholes, there will always be at least two pigeons in the same hole. But according to the team's quantum analysis, it is possible for none of the pigeons to share a hole.

The implications of the EPR paradox are important and shape our understanding of information and the fundamental physics of matter. Although it is too early to predict every implication, he believes that the quantum-pigeonhole principle could prove to be just as influential – if not more so. "This is at least as equally profound, if not more profound," he says. It implies a new concept of correlation that is surprising.

http://arxiv.org/abs/1407.3194

 

[sartsavaan]

Can I just try to make an analogy? If I consider myself a pigeon and find 2 anti-pigeons, we could actually all disappear.

 

[DrChinese]

http://arxiv.org/abs/1407.3194

"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. "

 

[DrChinese]

The quantum guitar principle:

If I have 6 guitars, I still need another guitar. That is because guitars obey Bose-Einstein statistics.

 

[microsansfil]

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

it's about http://www.newscientist.com/data/images/archive/2980/29802301.jpgThe Curious Quantum Mechanics of Pre- and Post-Selected Ensembles (1989)

Observation of a quantum Cheshire Cat in a matter wave interferometer experiment

could help to confirm or not "Seth Lloyd on the Universe as a Quantum Computer" ?

Patrick

 

[Nugatory]

The quantum guitar principle:

If I have 6 guitars, I still need another guitar. That is because guitars obey Bose-Einstein statistics.

There is a more powerful and general result that you can obtain through mathematical induction.

 

[atyy]

There is a more powerful and general result that you can obtain through mathematical induction.

:rofl:

 

[dm4b]

So I take it nobody else knows what to make of this yet either? ;-)

 

[microsansfil]

So I take it nobody else knows what to make of this yet either? ;-)

Surely people working on quantun computing :

http://iopscience.iop.org/1367-2630/16/5/053015/article
http://bcove.me/2mx7nmvw

Patrick

 

[HallsofIvy]

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".

 

[microsansfil]

Well, first, I take the "pigeon hole principle" to be a statement in mathematics, not physics, so this argument simply doesn't apply.

What is your point of view about "Observation of a quantum "Cheshire Cat" in a matter wave interferometer experiment" which also derived from mathematical statement ?

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.


Patrick

 

[RUTA]

What is your point of view about "Observation of a quantum "Cheshire Cat" in a matter wave interferometer experiment" which also derived from mathematical statement ?

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.Patrick

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.

 

[microsansfil]

My analysis of the quantum Cheshire Cat experiment is at
http://arxiv.org/abs/1410.1522

Thank you for this information.

Patrick

 

[Demystifier]

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

 

[Physics Monkey]

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.

 

[Demystifier]

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≥2 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≥2|ψ⟩=|ψ⟩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≥2,1−P≥2}\{P_{\geq 2}, 1- P_{\geq 2}\} we will always get the first outcome if the system has three particles and only two boxes.

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.

 

[atyy]

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.

 

[Demystifier]

Why don't some physicists accept contextuality?

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.

 

[Physics Monkey]

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.

 

[atyy]

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.

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

 

[Physics Monkey]

Because otherwise no one will make a thread about it :)

Indeed!

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

Quite curious. This seems to be in tension with the Pusey paper linked to above by Demystifier. I guess either there is a subtle terminological distinction or the new classical model is "contextual". Not that I know what these things mean.

 

[atyy]

Quite curious. This seems to be in tension with the Pusey paper linked to above by Demystifier. I guess either there is a subtle terminological distinction or the new classical model is "contextual". Not that I know what these things mean.

I haven't read both papers in detail, but it could well be that the new classical model is contextual. Roughly, one can think that the measurement disturbs the system, so that the outcome depends on the true properties of the system present before the measurement and the measurement process. So the outcome is not a true property of the system.

For example, the non-commuting canonically conjugate position and momentum are not true properties of the system in any hidden variable model. In Bohmian mechanics, the Bohmian position and Bohmian velocity differ from the quantum position and momentum. However, Bohmian mechanics is able to reproduce the quantum momentum distribution, because the measurement procedure disturbs the Bohmian velocity so that the distribution of outcomes represents quantum momentum, not Bohmian velocity.

Of course if we have a model of the true dynamics and the disturbance by assuming Bohmian mechanics, we can recover the Bohmian velocity from the quantum momentum, as done for example in http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/. Of course, we shouldn't assume Bohmian mechanics, since even within Bohmian-type theories, there isn't a unique dynamics consistent with quantum mechanics.

 

[atyy]

How's this contextual model for real pigeons? Let's say we have two boxes with an opening between them. Each box can fit at most two pigeons. I put two pigeons in one box, and one pigeon in the other box. The pigeons can hear me opening a box, and they are afraid of me, such that when I open a box, they always try to move into the other box. So when I look in anyone box, I will always see only one pigeon.

If I open both boxes, I will see three pigeons, and at least one box will have two pigeons.

 

[Physics Monkey]

I like your model very much.

 

[atyy]

Thank you. Now if only the opening between the boxes is also a wormhole ...

 

[Demystifier]

If I open both boxes, I will see three pigeons, and at least one box will have two pigeons.

There is a catch. If you perform weak opening of the boxes, you cannot simultaneously open them both.

The point is that weak measurement involves a post-selection, and you cannot make both post-selections at once. Or more precisely you can, but then you will just get the ordinary average value of the measured observable.

For instance, if a box contains either one or two (strongly measured) pigeons with equal probability, the average value of the number of pigeons in the box is 1.5. Of course, you cannot have 1.5 pigeons in a box in a single measurement. That's just the average value, i.e. the weak value without a post-selection. Likewise, the weak value with post-selection can also be thought of as a kind of "average value", with a difference that such a weak value can be anomalous. That's because the "probabilities" (or more precisely, weights) in the "average" may not be positive:
https://www.physicsforums.com/threads/range-of-weak-values.779551/

 

[Demystifier]

http://arxiv.org/abs/1403.2362

This paper has been criticized by several authors:
http://lanl.arxiv.org/abs/1410.8510
http://lanl.arxiv.org/abs/1410.0570
http://lanl.arxiv.org/abs/1410.0381
http://lanl.arxiv.org/abs/1409.8555
http://lanl.arxiv.org/abs/1409.5386

 

[RUTA]

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.

You're taking the approach in these two responses: http://www.math.umb.edu/~sp/pigeonco.pdf and
http://motls.blogspot.com/2014/07/three-pigeonholes-in-six-physicists.html

My response uses a different technical approach, but reaches the same conclusion -- the claim is false and is based on a flawed use of basic QM. I'll post my response after my colleagues have weighed in.

Someone asked what I thought of weak values in general. I must admit I have not studied them in general, only in response to specific claims. In doing so, I've found what I thought were two false claims (revealed in this thread) and one legit calculation (not necessarily interpretation) contained in this paper: Danan, A., Farfurnik, D., Bar-Ad, S., & Vaidman, L.: Asking photons where they have been. (2013) http://arxiv.org/abs/1304.7469. That exhausts what I know about weak values :-)

 

[atyy]

Is the quantumness of a weak value well defined? Is there anything like a Bell inequality which characterizes all local classical dynamics?

http://arxiv.org/abs/1305.7154
Understanding Quantum Weak Values: Basics and Applications
Justin Dressel, Mehul Malik, Filippo M. Miatto, Andrew N. Jordan, Robert W. Boyd

The above review mentions that there are some aspects of weak values that are classical, eg. http://arxiv.org/abs/quant-ph/0407155 and http://arxiv.org/abs/0906.4832.

It also says "Similarly, anomalously large weak values have been linked to violations of generalized Leggett-Garg inequalities that indicate nonclassical (or invasive) behavior in measurement sequences." So does it just mean "invasive" but in a way that can be local classical?

 

[atyy]

My response uses a different technical approach, but reaches the same conclusion -- the claim is false and is based on a flawed use of basic QM. I'll post my response after my colleagues have weighed in.

I must admit I have not studied them in general, only in response to specific claims. In doing so, I've found what I thought were two false claims (revealed in this thread) and one legit calculation (not necessarily interpretation) contained in this paper: Danan, A., Farfurnik, D., Bar-Ad, S., & Vaidman, L.: Asking photons where they have been. (2013) http://arxiv.org/abs/1304.7469. That exhausts what I know about weak values :)

Actually, in my exchange with Physics Monkey, I think we were thinking the claim in the paper of the OP (not the Danan paper) is technically right but use of English is bizarre. I guess this might be the same as you saying about the Danan paper that the calculation is legit, but not necessarily the interpretation.

 

[RUTA]

Actually, in my exchange with Physics Monkey, I think we were thinking the claim in the paper of the OP (not the Danan paper) is technically right but use of English is bizarre. I guess this might be the same as you saying about the Danan paper that the calculation is legit, but not necessarily the interpretation.

I think the quantum pigeonhole principle is false and their prediction for the outcome in the associated proposed experiment is wrong. Here is my analysis http://users.etown.edu/s/STUCKEYM/QuantPigeonhole.pdf.