# Why is quantum entanglement special?

1. Jun 13, 2012

### mieubrisse

Clearly, I am a newb at this. However:

I was reading a bit on qubits and quantum entanglement and -- though I know that QM has no analog to classical mechanics -- the general concept seems to be: two particles interact and become quantum entangled, and then have non-local ties to each other. To me, this sounds kind of like "An immensely tiny billiard ball spinning one direction along an arbitrary axis comes into contact with another stationary ball in a deserted place. Nobody has any idea which direction the balls are spinning in. The two balls are then given to two separate researchers (the researchers have special ideal-environment cubes to contain the balls during transport so they have ZERO effect on the balls). When a researcher determines which axis and direction one of the two billiard balls is spinning along, the other researcher is guaranteed to find that the other billiard ball is spinning along the same axis in the opposite direction.

But of COURSE the researcher was guaranteed to find that the other ball is tied to the first because we know that the first ball will change the state of the second in a known way (in this case, friction between the balls causes the originally-stationary one to move on the same axis as the first in an opposite direction). Seemingly, if we know how the balls came in contact and know that they were not affected in any way since the initial contact (the analog to quantum decoherence??), we can accurately predict the entire system based on one measurement.

I'm sure it's not that simple.... what did I miss? Why is quantum entanglement so surprising and magical?

Best,
mieubrisse

Last edited: Jun 13, 2012
2. Jun 13, 2012

### Simon Bridge

That's what everybody thinks at first but the stats work out differently.
Look up "Bell's Inequality".

It is the degree of the correlation between entangled particles over repeated measurements that is special.

3. Jun 13, 2012

### sheaf

For a clear exposition of the entanglement weirdness I always recommend the "Quantum Mechanics in your Face" lecture by the inimitable Sid Coleman. It describes a simple thought experiment which nicely highlights the surprise quantum mechanical correlation.

4. Jun 13, 2012

### lugita15

mieubrisse, when most people hear about quantum entanglement, this is exactly what they believe the explanation to be. Einstein himself believed that this kind of "local hidden variables" explanation was enough to account for entanglement. But then JS Bell proved his famous theorem, which says that entanglement possesses certain properties that are incompatible with such explanation. Bell's Theorem and the reasoning behind it are absolutely fascinating. You can read about it in this excellent article:
http://quantumtantra.com/bell2.html

5. Jun 13, 2012

### DrChinese

Welcome to PhysicsForums, mieubrisse!

As already mentioned, this is the EPR view. Bell came later, and that is where the magical part comes in.

For the angle settings analogous to your example, you are correct. You might expect such results. But at other angle settings, the relationships don't hold up. Read about Bell, and then come back with some more questions!

6. Jun 14, 2012

### Simon Bridge

This comes up so often I feel I need to work out some example that does not lend itself to the classical idea... and make it explicit. Coleman's lecture looks like it could contain one ... I'll have to look more closely.

Its tricky - to see what I mean: Herbert's description of twin light in his article
Each photon's polarization depends on the other's polarization but that polarization in turn depends on the first. This mutual dependence renders each photon polarization completely indefinite subject to the system-wide rule that should a situation ever arise (say in a measurement) that one photon acquires a definite polarization, then the other photon--no matter how far away--must instantly take on that same value for its polarization.
... leads itself to the counter-argument that the two photons just decided which polarization to have while they were still close together - that way, completely classically, it wouldn't matter how far away they were, a measurement of one allows us to deduce the state of the other.

This is about where most popular description leave off ... but it is the statistics in the resulting experiment that is important. The kicker is the "code mismatch" observation at the end - which nicely ties the experiment with Bell's inequality.

Even so - I'm not sure of his math - after all, in his example #4 the detectors are aligned 60deg to each other - wouldn't you expect a 75% mismatch in that situation - classically? (By his argument - aligning the detectors at 90deg to each other would be 3x30deg for 3x25% = 75% mismatch or less - but reality give 100% mismatch - but we know that crossed detectors means they never agree!)

I've misread it or there's a missing assumption. How do we close off this line of reasoning without going all hand-wavey?

Coleman seems to have one of the keys - most description make some statement about faster than light communication (eg. Herbert - above) when this is actually the opposite of what is meant: FTL is only needed for the classical description (he says).

But I only went through the lecture once so far: it has a high information density for this sort of lecture, he is a messy speaker (pretty much normal for an academic), the transparencies are hard to read, and the audio cuts out at annoying times. It is amazing the lecture is as understandable as it is.

He also has randomly aligning detectors too, and relies on the observed vs predicted statistics - but makes the nature of the separation part clear.

refs (repeated so you don't have to go back and hunt for the links)
Coleman: "QM IYF"
Herbert: "Simple Proof"

7. Jun 14, 2012

### sheaf

You're right - the audiovisual quality isn't great. If it helps, there's an exposition of Coleman's thought experiment here.

8. Jun 14, 2012

### ThomasT

Quantum entanglement is a lot like what you imagine it to be, I think. Underlying disturbances interact or are emitted via the same atomic process, then they exhibit relationships which are understandable via classical principles (eg., conservation of angular momentum). The correlations in optical Bell tests are quite expected vis the historically observed behavior of light wrt crossed polarizers. That is, there's nothing surprising or magical about the correlations. But you will not be able to fashion a local hidden variable model of quantum entanglement in line with Bell's formulation. What this means has been a matter of conjecture for over 50 years and is still unresolved in terms of the consensus of scientific opinion.

But one thing is certain, I think, and that is that quantum entanglement correlations are not surprising, and certainly not weird or magical.

Last edited: Jun 14, 2012
9. Jun 14, 2012

### mieubrisse

Wow, thank you all for such quick and thorough responses! I was able to get time enough today to read the Herbert article (I'll get to the Coleman video tomorrow), and with all seriousness when the revelation about the angles came out, I got shivers. Actual physical shivers.

Because that just SHOULDN'T happen! But it does! What in the whole wide world is going on with this reality? But that leads me to my next question, and one that Herbert leads the reader to ask. If I understood the article correctly, Bell's proof is untouchable. What he has proved is complete and 100% solid, and will never die. Quantum theory (a somewhat abstract term in the article's way of putting it) on the other hand ISN'T as absolute. Now, quantum theory predicts that we will never see non-local facts, only non-local theory due to our underlying non-local reality. So my question is thus: WHY is reality non-local when everything we see is local?

Have I followed the article correctly? I'll undoubtedly need time to fully digest what I read, but I think I have the gist of it even though a complete understanding isn't there yet.

On a related note, what does the community think of this article (the one that got me started on this quantum adventure):

http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2007/01/21/ING5LNJSBF1.DTL&ao=all

10. Jun 14, 2012

### DrChinese

Great question!

There are interpretations in which there is nothing non-local in the Bohmian sense of non-local. For example, the Time Symmetric class of interpretations allow a future context to be part of the equation. In these, locality is respected but classical causality is not.

11. Jun 14, 2012

### FieryJack

Another noob here and my original question was the same as mieubrisse's, so thanks to you guys for some excellent references. I ordered my calcite today!

Non-local reality: would this not imply that all particles are entangled with each other - the difference being a matter of degree?

12. Jun 14, 2012

### DrChinese

Welcome to PhysicsForums, FieryJack!

I cannot answer that particular question, but perhaps our Demystifier will tackle it. He always has a good take on the non-local side of things.

13. Jun 14, 2012

### ThomasT

It isn't known that reality is nonlocal. Some physicists and philosophers infer that it is, and some don't.

Just because you can make an explicitly nonlocal theory doesn't mean that nature is nonlocal, and just because you can't make an explicitly local theory (a la Bell) doesn't mean that nature isn't exlusively local.

The gist of it is that interpreting arguments like Bell's and Herbert's is somewhat complicated and still a matter of debate, and the bottom line is that there's no physical evidence for the existence of nonlocal propagations in nature.

Retrocausality ...

But keep in mind that I'm just a layperson also (albeit one who's studied enough of this stuff to have certain opinions about it), and my take on these considerations might change as I learn more. It's best to pay most attention to what people like DrC, Demystifier, et al. have to say about these issues, imo.

14. Jun 15, 2012

### Simon Bridge

Retrocausality is one of the fun results from attempts to reconcile quantum mechanics with relativity. The trick is coming up with an experiment ... afaik: it is purely theoretical right now.
eg.
http://sydney.edu.au/time/conferences/retrocausal_models.html
... I think you'll need at least senior undergrad quantum mechanics to see what they are going on about... but the abstracts will give you useful starting points for your own searches.

The news article looks like it is confusing things ... as usual. As a rule of thumb - treat all press pronouncements about science as highly suspect. eg, it is unhelpful to think of entanglement experiments as involving FTL communication.

15. Jun 15, 2012

### micky_gta

Something that will help is to stop thinking like a materialist. Accept that there are more things going on than your main senses can detect.

"Imagination is more important than knowledge."

- Einstein

16. Jun 15, 2012

### ThomasT

@ mieubrisse,

Quantum entanglement is mysterious in that, as DrC and others mentioned, nobody has, and QM doesn't provide, a precise qualitative understanding of it. But I don't think there's any reason to call it magical or weird. It more or less obviously has to do with relationships between the measureable motional properties of entangled disturbances, because that's what entanglement experiments are designed to produce.

Anyway, by way of clarification, the term quantum nonlocality doesn't mean the same thing as classical nonlocality. Classical nonlocality refers to either action at a distance, which is just a contradiction in terms, or faster than light propagations. Quantum nonlocality refers to (note the quote following the citations):

Experimental study of a subsystem in an entangled two-photon state
Dmitry V. Strekalov, Yoon-Ho Kim, and Yanhua Shih
Phys. Rev. A 60, 2685–2688 (1999)

http://arxiv.org/abs/quant-ph/9811060

17. Jun 16, 2012

### vanhees71

I do not know, what you mean by "qualitative" understanding. Perhaps you mean intuition, and of course, we don't have an intuition about entanglement, because in everyday life we don't have experience with such phenomena. The reason is that we are surrounded by macroscopic systems, with an overwhelming number of coupled microscopic degrees of freedom. Fortunately, our senses coarse-grain over all the many unimportant microscopic details, and the relevant macroscopic observables behave to a utmost high accuracy according to the laws of classical physics. That's why we have found the classical description of nature before we knew about the quantum nature behind. The only way we can understand quantum theory is through mathematics and the "mapping" between mathematical abstract structures (Hilbert-space vectors, statistical operators, and operators representing observables, etc.) to the real world (Born's probability rule for the interpretation of quantum mechanical states, spectral theory of operators).

If it comes to non-locality one has to be a bit careful, what one means. The most comprehensive quantum theory we have today is relativistic quantum field theory, which is by construction a theory of local interactions. All causal actions are thus described by local interactions. "Local" means here that we describe systems of elementary particle with a set of field operators and a Hamiltonian that is derived from the spatial integral over polynomials of field operators at the same space-time point. The field operators also fulfil local transformation laws under proper orthochronous Lorentz transformations.

Using such a description of a quantum system implies the socalled "linked-cluster principle", which states that experiments on systems that are very far away from each other are stochastically independent, i.e., the probabilities for different local subsystems at far distances factorize.

On the other hand, quantum states can describe non-local correlations, and that's what's commonly discussed when it comes to entanglement. E.g., nowadays quantum opticians can easily produce entangled two-photon states. The important point is that these are real two-photon states, i.e., a Fock state with a precise photon number of two. The entanglement of the photons in such a state, usually produced with help of parametric down conversion by shooting a laser through a birefrigerent crystal, are entangled with respect to their polarization state. This we cannot describe with everyday language, and we have to go to the level of mathematics. The state, I have in mind is of the form

$$|\psi \rangle=\frac{1}{\sqrt{2}} [|HV \rangle-|V H \rangle].$$

I've noted only the polarization part of the single-photon states, and I use the usual shorthand for tensor products $|H V \rangle:=|H \rangle \otimes |V \rangle$.

In principle, for the following discussion, I'd have to also note the spatial part of these states, but that's cumbersome, and I hope I can make clear my point of view in this somewhat simplifying notation.

The point is that this photon state is prepared at the very beginning using a local device, namely the crystal for the parametric down conversion. Then the two photons propagate without further interactions, and after some time the spatial probability distribution for measuring one of the photons is peaked at very far distant positions (note that I don't talk about positions of photons, which cannot be defined in a simple way, but that's not so much an issue here). So Alice and Bob put far distant photo detectors with polarization filters in the direction of these two spots of high probability to detect a photon. Each of them measures single photons.

First of all we may ask about the probability that, say, Alice detects a photon with a certain polarization, if her polarization filter is directed in horizontal direction. This is described by the socalled reduced statistical operator for the one-photon subsystem. With the above given state, Alice thus describes the state of her one photon as

$$\hat{\rho}_{A}=\text{Tr}_2 |\psi \rangle=\frac{1}{2} \hat{1}=1/2 (|H \rangle \langle H | + |V \rangle \langle V|).$$

This means, she has a totally unknown polarization state. If she samples very many photons, using all angles of her polarization filter, she'll come to the conclusion that she simply has an unpolarized photon source. The same holds true for Bob. Both cannot conclude that their photons come from a single source of entangled photon pairs with their local measurements alone.

Now they can also measure the time of their photon registration. Now suppose that Alice points her polarizer in H direction and Bob his in V direction. Then our entangled state is such that whenever Alice registers a photon (which is, of course, only in 50% of all produced photon pairs) also Bob must register his photon (assuming detectors with 100% efficiencies) too. That means there is a 100% correlation between Alice's and Bob's polarization state of their photons, although the polarization state of each of their photons is maximally random (unpolarized photons!).

Now, this experiment has been done such that the registration events were spacelike. According to relativity thus there cannot be any causal effect of Alice's photon detection on Bob's and vice versa. Thus, the non-local correlation cannot have been caused by Alice's or Bob's measurement, and the above description of the quantum theoretical analysis should make it very clear that such an assumption is not necessary to make at all. In this minimal interpretation, there is no necessity for a "collapse of state" or any other mysterical "spooky action at a distance". This is only due to the collapse interpretation of the Copenhagen and related schools of quantum theory. If one sticks to the minimal necessary assumptions, i.e., Born's probability rule as the interpretation of the quantum-theoretical states, no such assumptions have to be made, and there is no contradiction between quantum dynamics and Einstein causality, according to which no signals can propagate faster than with the speed of light. Thus also the criticism by Einstein, Podolsky, and Rosen against quantum theory becomes immaterial. According to the Minimal Interpretation, of course, nature is inherently probabilistic, i.e., indeterministic. An observable has only a determined value if the system has been prepared in an eigenstate of the corresponding operator, describing this observable. Otherwise this observable doesn't have a determined value, and you can only give probabilities for the outcome of measurements of this observable. That's it.

Whether you consider this as a "complete description" of nature or not, is your own belief. It has nothing to do with nature which behaves as it behaves. Physics states as precisely as it can facts about phenomena in nature and tries to describe this behavior with mathematical theories. In this way you can make predictions about the probabilities of measurements, given a previous preparation of the system. Experiments have then to use ensembles of independently prepared systems and get, within the statistics of the experiment, the probabilities for measuring the values of the observables of such prepared ensembles and compare it with the the quantum-theoretically predicted ones. So far, quantum theory has survived all tests to a very high precision. Also the non-classical features of entanglement with their non-local correlations that cannot be described by classical local hidden-variable theories (Bell's and related inequalities), have been confirmed with a huge significance. In this sense we must come to the conclusion that quantum theory is indeed a complete description of nature and from this we must conclude that nature is inherently non-deterministic.

18. Jun 16, 2012

### ThomasT

I think there can be an intuitive approach to understanding quantum entanglement, even without a qualitative (ie., visually descriptive) understanding of what's happening at sub-instrumental levels. For example, one of the key concepts wrt entanglement has to do with the conservation laws, at least some aspects of which are visually describable/understandable (eg., conservation of angular momentum), and which are retained in the QM treatment of entanglement.

Yes, that's why I referenced the quote from the paper that I linked to in the post before yours.

I'd just say that QM gives as complete a quantitative account of quantum instrumental phenomena as is currently possible. I don't think anything can be concluded about what nature inherently or fundamentally is or isn't sub-instrumentally.

Wrt quantum entanglement, certain obstructions are filtering/measuring the relationship between some property of the motion of entangled entities. Some concepts from our everyday sensory apprehension of the world do seem to apply to this situation.

Last edited: Jun 16, 2012
19. Jun 16, 2012

### the_pulp

Vanhees71 your explanation was very enlightening, but I still cant see how a local theory like QFT can be consistent with entanglement. The only way I see it is by assuming that the two particles "negociate" which values they are going to choose if any pair of experiments are performed on them, but this seems "hidden values" like, and Bell inequalities is against it. So what am I loosing???

Thanks

20. Jun 16, 2012

### Simon Bridge

If you watched the Coleman lecture - the setup there involved only local interactions but produced results that allowed Coleman to claim non-locality.

You can get a good intuitive picture of entanglement processes the same way you can get a good intuitive picture of formal dinner parties: by becoming familiar with them. They are different right down to the logic. If you try to get a feel for them by analogy, it won't work... the analogies are just to make the hard-of-thinking feel better.

You clearly like to question and challenge - so you will not be happy with an analogy. In fact, you seem the sort who won't be happy with the actual physics as it stands either and will itch to advance it. You'll find physicists like to encourage that kind of thing: science is a work-in-progress, after all ...