# What's so unusual about entanglement?

1. Nov 5, 2015

### franklinhu

Why does this whole quantum entanglement thing impress anybody?

When you look at articles in the lay press, they tell you that there is an "instantaneous" communication from one particle to another. But as these posts clearly show, there is no communication involved at all. There is just this "correlation" that when you look at one particle, you know what the other one is. This happens as a process of deduction, not communication. If you have two gloves and you send the left one to Seattle and the right one to Boston, when you open the one in Boston and see it is a right glove, you know instantly that the one in Seattle is the left glove. Why do you know? Because gloves come in pairs left/right. If you have the right, then then the left one is elsewhere. Simple deduction, no instantaneous communication between Seattle and Boston required.

But yet, the popular press keeps on pushing this idea that there is some kind of instantaneous "communication" going on. What is worse is the implication that if we change the state of one particle, it is instantly reflected in the other - so not true. Not even the published papers make this wildly wrong claim. Obviously no communication is possible since you're just looking at the right glove in Boston, you can't turn it into a left glove and have the right glove show up in Seattle. It doesn't work that way.

So given that, why are physicists so impressed with something so obvious and completely useless for any practical purposes?

And why does the press keep on insisting this has something to do with instantaneous communication?

2. Nov 5, 2015

### Truecrimson

This is a misunderstanding of quantum entanglement. The outcome is random and correlated not just for a particular measurement but for all possible measurements one could make. For pure quantum states, this always allows a violation of Bell's inequality which no classical correlation can do.

3. Nov 5, 2015

### Strilanc

Entanglement does have useful purposes (though perhaps not practical). You can win some coordination games more often if you have entangled qubits available as a resource. In a classical universe this would imply you were cheating by secretly communicating. But entanglement doesn't allow you to communicate. But classically it would require communication. But quantumly it doesn't enable communication. (But repeat.) That's the paradox.

4. Nov 5, 2015

### f95toli

Also, entanglement DOES have practical applications. The obvious examples is quantum key distribution which is already used commercially and will probably see more widespread use over the next few years. There are plans to roll this out to point-2-point encrypt whole communication networks and it might also be possible to use this for encrypted near-field communication for "tap to pay" type services..

5. Nov 7, 2015

### Staff: Mentor

If that were all there was to it - one observer measures spin-up on a given axis, the other must measure spin-down because entangled particles come in up/down pairs just as gloves come left/right pairs - you would be right and entanglement would be no big deal.

But that's not all there is to it.

Consider a pair of entangled spin-1/2 particles; we create the pair and then send one member of the pair to each of two observers (traditionally named Alice and Bob). Suppose they measure the spin along different axes? Quantum mechanics says, and experiment confirms, that if Alice measures spin-up on her axis, then the probability that the Bob will measure spin-up on his axis is $\sin^2\frac{\alpha-\beta}{2}$ where $\alpha$ and $\beta$ are Alice's and Bob's angle settings. You can verify that when they both use the same angle the probability of them both getting the same result is zero, just as with the gloves.

Now if you look at the formula you will notice somethingly profoundly weird about it, something that doesn't happen with the gloves: if Alice changes the angle at which she chooses to measure, it will change the probability of Bob getting a given result even though he hasn't changed anything in his setup. Alice can even change her setup while the two particles are in flight and Bob and Bob's particle are light-years away, with Bob's particle just centimeters away from his detector - and Bob's probabilities will change. That's what makes entanglement interesting.

It is possible to prove (google for "Bell's theorem", and check out the web site maintained by our own DrChinese) that if QM is correct Bob's results cannot be determined just from the setting of his detector and the properties the two particles had when they were created. One way or another, you have to include Alice's setting as well.

Last edited: Nov 7, 2015
6. Nov 7, 2015

### vanhees71

What you can read in the lay press about quantum theory is almost always wrong. Entanglement is, indeed, a feature of the quantum-theoretical world which is most distinct from anything we have in terms of classical physics, which is always local and realistic.

This means that in classical physics you have a one-to-one mapping of physically observable quantities with the mathematical "objects" of the theory, which are fields (the classical electromagnetic field, energy-momentum-stress and angular-momentum tensors of macroscopic matter distributions). The interaction between these objects are always local in the sense that there are no actions at a distance. The physical laws are causal and deterministic in the strict sense. Causality means that there is an arrow of time inherent in the space-time structure and all dynamical physical laws are formulated in the sense of cause-effect relations, e.g., you have a given charge-current distribution, which are the sources of the electromagnetic field, which in turn acts back to the charge-current distribution, and you have a self-consistent set of equations of motion describing this in a cause-effect sense. The interaction is always local in the sense that the force density is determined by a local functional of the electromagnetic field. The theory is also deterministic, which means that if you know the state of the system, i.e., the field configurations exactly in the past you can calculate them for any later time, and the knowledge of this state of the system implies the precise knowledge about any outcome of measurements you can do on this system.

Quantum theory, i.e., relativistic quantum field theory and the Standard Model is different. It is still causal and interactions are local, but it is not deterministic. Already the complete knowledge about the state of the system does not imply that you know the outcome of all measurements. To the contrary, if you prepare a system like an electron such that e.g. its position is pretty precisely known (you can never know it really precisely!) this necessarily implies that its momentum is quite unknown. The only thing you know about this electron, even when you have prepared it, what quantum physicists call a pure state, which is the most precise preparation you an make in principle. This has nothing to do with some technical problem to measure the electron's momentum precisely or to manipulate the electron in a way to determine it precisely; it is just not a property of an electron that it can have a well determined position and momentum at the same time.

The interactions in the standard model are still local by construction, i.e., you build in locality (the technical term is micro-causality) from the very beginning of constructing the maths of the model. This implies that it is impossible within the theory to communicate in any way with signals that propagate faster than the speed of light in a vacuum.

At the same time you can have long-ranged correlations between far distant parts of a system. The most common example are pairs of entangled photons. Photons are quanta of the electromagnetic field, and nowadays the quantum opticians can produce two-photon states that have entangled polarizations by shooting a laser into a certain sort of crystal to create such two photons by absorbing a photon from the laser field and emitting two new photons, each with half of the energy of the laser photon. The total polarization of the two photons is 0 (determined feature of this two-photon state). The polarization of each of the two photons alone is maximally indetermined, i.e., when one observer (usually called Alice) is measuring the polarization of her photon, she gets with 50% probability that it's horizontally and with 50% probability that it is vertically polarized.

This is another feature of quantum theory: Even if you know the precise (pure) state of the two photons as a whole, you may have minimal knowledge about other observables that are not determined by the state, representing the corresponding preparation procedure of the pure two-photon-polarization state. The only thing you know about the polarization of Alice's photon are probabilities, and in this case the single-photon state is represented by the state of minimal knowledge in the sense of information theory.

The same is true for the other photon in the two-photon state. Since the momenta of the two photons are back-to back you may wait long enough by putting two detectors far away from the two-photon source, so that the two photons are registered very far away from each other. As long as the photons do not interact with anything else, they still stay in this pure two-photon state you began with. Both photons (Alice's and the other one detected by Bob) are "unpolarized", i.e., if you measure a lot of single-photon polarizations with identically prepared entangled photon pairs both Alice and Bob find with 50% probability horizontally and with 50% probability vertically polarized photon. There's no way to predict the outcome of these polarizations, and according to quantum theory indeed each of the photons in the pair do not have a determined polarization state at all.

Now you can keep track of which photon measured by A belongs to the photon from the entangled pair measured by B by just very precisely noting the time when A and B register their photons. Then it turns out that whenever A finds a H-polarized photon B necessarily finds a V-polarized photon! Although the single-photon polarizations are maximally undetermined, there's still a 100% correlation between them!

But that's not the most curious property of quantum theory! If Alice and Bob adjust their polarizers in certain relative angles and if they do statistics about some very specific polarization observables they find something which is mathematically proven to be impossible in any local deterministic theory. This is the violation of the famous Bell inequality, which holds for any local deterministic description of the photons. The idea behind this is that it could well be that the photons have some properties we simply don't know, i.e., there are socalled hidden variables that determine each of the photons' polarization, but we simply don't know these, and that's why the polarizations appear to be "random", but only because we don't know the values of the hidden variables. The violation of Bell's inequality rules out, however, any locally realistic description of the photons' polarization. At the same time the very precise measurement of this violation of Bell's inequality matches the predictions of quantum theory with the same precision.

The conclusion is that the world is for sure not describable entirely in terms of local realistic theories. It may be that one day somebody finds a non-local realistic theory, but that's very difficult, because at the same time you must avoid the violation of relativistic causility, i.e., one cannot simply assume that signals are exchanged faster than with the spped of light between the two photons when measured by A and B at a far distance apart without destroying the causality structure of relativistic spacetime. This also implies the assumption of a "collapse of a state", which are (in my opinion unnecessarily) assumed in some interpretations of quantum theory.

7. Nov 7, 2015

### PeroK

Nothing is useless! Everything can be turned to some purpose or other.

8. Nov 7, 2015

### DrChinese

It's not communication. However, when you collapse one member of an entangled system, the remaining member(s) are affected immediately. With an entangled pair, this can be easily demonstrated. No one understands the precise mechanism. But it is not classical (local and realistic).

As to obvious: entanglement was known by 1935. But it was not until 30 years later that Bell figured out the peculiar attributes of entanglement that led to his famous Theorem. That was the watershed moment in understanding the fuller implications of entanglement.

9. Nov 7, 2015

### Atla

Maybe it's such a big deal because it's the Western common sense to think that the universe is made up from separate things, like objects, quantum systems, etc. We take the everyday illusion of separateness for granted. But that is merely an unproven philosophical assumption, maybe of Greek and of Biblical origin.

An alternative view may for example be that everything is one, meaning that everything is entangled with everything else in this universe (otherwise none of this could be happening anyway). And we can track "immediate" entanglements for a while.

10. Nov 7, 2015

### vanhees71

Well, if there's no collapse, there's nothing to understand about it. For me that's the most simple solution of this "problem", but now we entering metaphysics again, and too much of that is not healthy in physics ;-)).

11. Nov 7, 2015

### zonde

Just correlation does not violate Bell inequalities. That's the big deal about entanglement violating Bell inequalities.
So you can't scientifically model a situation where Bell inequalities are violated without communication between parties.
But then (loophole free) experimental confirmation of violation of Bell inequalities falsify claim of relativity that nothing can move faster than light.

So you close your eyes and hope that there is some loophole in that chain of reasoning.

12. Nov 8, 2015

### vanhees71

The Bell inequality is violated according to standard quantum theory, and this precisely implies that there's no "communication" between the particles necessary to make up the quantum correlation (which is stronger than any correlation that's describable by a local realistic theory) described by entanglement. The correlation is due to the preparation of the entangled state and not due to the measurement (on an ensemble of identically and independently prepared systems!) to reveal this correlation by measurement. What's true is that you need to compare the measurement protocols between the two parties (Alice and Bob) to find out about the correlations, but that has nothing to do with the quantum nature of entanglement. That's just usual "classical" communication between A and B.

13. Nov 8, 2015

### zonde

If we take clicks in detectors as objective facts of reality then what you say is not true as proved by Bell. Do you agree?

14. Nov 8, 2015

### DennisN

An introductory lecture which may be interesting to see: Anton Zeilinger - Quantum Information and Entanglement, which includes descriptions of experiments and applications.

15. Nov 8, 2015

### Staff: Mentor

It's worth taking a moment to say exactly what is meant by "communication" here. Whatever it is, it can't be causal, because when the two measurements are spacelike-separated we can interpret the correlation either as Bob's measurement influencing Alice's or as Alice's measurement influencing Bob's.

16. Nov 8, 2015

### vanhees71

No, I don't. The clicks are just registering the photons and the outcome is according to quantum theory, violating Bell's inequality in accordance with the predictions of quantum theory. It does not say that there is a faster-than-light signal between the two "click events", of put differently, the correlation in there (objectively!) according to the preparation in an entangled state, long before the clicks but not due to faster-than-light signals between the "click events". A collapse interpretation is not necessary and in my opinion violates basic principles like causality and thus I think one should abandon them from the interpretation of the theory. It's metaphysics anyway and more in the realm of personal belief than scientific facts.

17. Nov 8, 2015

### zonde

Vanhees, please understand that it does not matter what quantum mechanics says. Loophole free experimental (by clicks in detectors) violation of Bell inequalities plus Bell theorem is all that is required.

18. Nov 8, 2015

### zonde

You are using symmetries of relativity to analyze a situation that contradicts relativity. It won't work of course.

19. Nov 8, 2015

### vanhees71

I don't understand, what you want to say. This does not prove that there's faster-than-light communication between the two photons or the measurement devices. The findings can be explained with standard quantum field theory, and that is by construction microcausal. So there's no necessity to give up Einstein causality, but local realism.

20. Nov 8, 2015

### zonde

Indeed experiment + theorem proves that faster-than-light communication is the only scientific explanation.

This contradicts Bell theorem so there has to be error in that reasoning.
I have no doubt about Bell theorem being correct.