How is quantum entanglement different to classical pairing?

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I find it difficult to follow the analysis on experiments that investigate quantum entanglement, there seems to be something fundamental about quantum entanglement that I am missing.

Perhaps if I step through a simple example, it will show up what it is that I am misunderstanding.

Say a source of entangled photon pairs are used in an experiment, such that the photons pass through two vertically orientated polarizing filters, positioned either side of the photon source, with one filter slightly further away from the source than the other. For the sake of simplicity, it is assumed that the polarizing filters are perfect - that any photons that make it through are polarized to the orientation of the polarizing filter.

For the photon of an entangled pair that reaches its filter first, its wave function collapses and its orientation is at some, random angle to the filter. At that same moment, the other photon collapses its wave function too - and its orientation is at 180 degrees to the other photon's orientation.

The probability of a photon passing through a filter is dependent on its angle of orientation, and with an equal probability of any angle occurring, 50% of the photons will make it through the filters, and 50% of photons will fail to make it through the filters.

Except for the special cases when the photons are at 0 degrees to the filters, or at 90 degrees to the filters - where either both photons pass through the filters, or both photons fail to make it through the filters, there is a probability of whether a photon is absorbed or not, based on the angle of the photon's orientation to the filter. In these cases, there is no guarantee that if one photon of the pair makes it through its filter, then the other photon will too, and vice versa.

So how is this different to the classical view, where the photon pairs are emitted with an orientation that is at some random angle to the filters, with the orientation of the two photons being at 180 degrees to each other? Or is it, that for this particular set up, there is no difference between the two explanations?

Edited by robinpike
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(Note: orthogonal, or "opposite" polarizations are at 90º, not 180º)

If you have an entangled pair, you know the correlation of the polarizations, but not the polarization of a particular photon until it's measured. So saying 50% make it through the filter is inot the whole story. That's true if you have a known polarization passing through a filter that's at 45º to that polarization. But that also applies to the second filter as well — 50% chance of making it through. But that means 25% of the time you get both photons, 25% of the time you get no photons, and half the time you get one photon at one detector but not the other. The photon polarizations are not correlated.

If the photons are entangled, you always get the second photon, if you detect the first one, and never get the second photon if you don't get the first one.

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I find it difficult to follow the analysis on experiments that investigate quantum entanglement, there seems to be something fundamental about quantum entanglement that I am missing. (...)

You love this entanglement.. Don't you?

While IMHO you should pay more attention to learn entire quantum physics in the first place..

(Swansont's example, mixing degrees 90/180)

Especially in areas easy to perform the real life experiment at home..

(...) where either both photons pass through the filters, or both photons fail to make it through the filters, there is a probability of whether a photon is absorbed or not, (...)

No, polarization filter doesn't absorb substantial quantity of photons.

They are passed through (like in transparent object), or reflected (like in mirror).

If it would absorb them, polarization filter would melt (actually happened to me, but my fault, too strong laser used, for too long time, with plastic polarization filter).

This is one polarization filter, with blue laser.

If I would put second polarization filter, and point laser such a way to pass light through both of them,

you could see intensity of spots after second "split" would be smaller.

Second polarization filter could be rotated, and observed how intensity changes during rotation..

There could be placed 3rd, 4th, and so on, polarization filter there. Each one could be rotated independently.

You could make the real life experiment, to gather the real life experience in the subject..

And then show them on video/photos. With results put to OpenOffice SpreadSheet.

Light intensity read by some device and/or photodiode/photoresistor/etc.

Edited by Sensei
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(Note: orthogonal, or "opposite" polarizations are at 90º, not 180º)

If you have an entangled pair, you know the correlation of the polarizations, but not the polarization of a particular photon until it's measured. So saying 50% make it through the filter is inot the whole story. That's true if you have a known polarization passing through a filter that's at 45º to that polarization. But that also applies to the second filter as well — 50% chance of making it through. But that means 25% of the time you get both photons, 25% of the time you get no photons, and half the time you get one photon at one detector but not the other. The photon polarizations are not correlated.

If the photons are entangled, you always get the second photon, if you detect the first one, and never get the second photon if you don't get the first one.

Thanks Swansont. Is it possible to perform the experiment such that the photon pairs can be detected as individual hits on their respective photon detectors and therefore the hits correlated as being from the same photon pair? If so, then entanglement will produce pairs of hits being detected at the same time (for a perfect experiment, entanglement will produce detection at the same time or both detectors nothing). Whereas classical pairing will, as you mention, produce 25% of the time you get both photons, 25% of the time you get no photons, and half the time you get one photon at one detector but not the other.

Assuming the above to be correct, has this type of experiment be performed? If so, did it demonstrate entanglement or classical pairing?

Edited by robinpike
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[..]

While IMHO you should pay more attention to learn entire quantum physics in the first place..

[..]

No, polarization filter doesn't absorb substantial quantity of photons.

They are passed through (like in transparent object), or reflected (like in mirror).

[..]

Don't you know Polaroid sunglasses? They mostly absorb the light that is blocked.

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Thanks Swansont. Is it possible to perform the experiment such that the photon pairs can be detected as individual hits on their respective photon detectors and therefore the hits correlated as being from the same photon pair? If so, then entanglement will produce pairs of hits being detected at the same time (for a perfect experiment, entanglement will produce detection at the same time or both detectors nothing). Whereas classical pairing will, as you mention, produce 25% of the time you get both photons, 25% of the time you get no photons, and half the time you get one photon at one detector but not the other.

Assuming the above to be correct, has this type of experiment be performed? If so, did it demonstrate entanglement or classical pairing?

Yes, that's pretty much exactly the experiment that has been done, many times. Since entanglement is still part of mainstream physics, what do you think the result was?

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Yes, that's pretty much exactly the experiment that has been done, many times. Since entanglement is still part of mainstream physics, what do you think the result was?

I've only seen results that support entanglement... but those experiments do not have the polarizing filters at the same angle. Those experiments typically have the polarizing filters at a difference of 120 degrees and Bell's inequalities are used to assess if the results agree with entanglement or classical pairing. The analysis of those experimental results are complex to follow.

Since entanglement versus classical pairing predicts different results when the filters are at the same angle, does anyone have a reference to those experimental results? Those results will be easy to analyse.

Indeed, why is it even necessary to devise a complicated experiment involving Bell's inequalities?

Edited by robinpike
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I've only seen results that support entanglement... but those experiments do not have the polarizing filters at the same angle. Those experiments typically have the polarizing filters at a difference of 120 degrees and Bell's inequalities are used to assess if the results agree with entanglement or classical pairing. The analysis of those experimental results are complex to follow.

Those are Bell tests, for excluding local hidden variables. Entanglement is also used, for example, for quantum teleportation experiments.

Since entanglement versus classical pairing predicts different results when the filters are at the same angle, does anyone have a reference to those experimental results? Those results will be easy to analyse.

I don't have any handy. Maybe when I'm back at work.

Indeed, why is it even necessary to devise a complicated experiment involving Bell's inequalities?

Because it's a complicated situation.

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Since entanglement versus classical pairing predicts different results when the filters are at the same angle, does anyone have a reference to those experimental results? Those results will be easy to analyse.

Indeed, why is it even necessary to devise a complicated experiment involving Bell's inequalities?

Bell's test was devised to show that EPR's idea of local hidden variables was incorrect. Simple tests that show a difference between classical predictions and quantum mechanical measurements would still fall foul of EPR's claim that the results could flow from some non-classical but still locally hidden variable. What was Bell's genius was to realise that a simple statistics test can show the possibility of a set of data ie which distribution of results can theoretically be produced from a single joint distribution.

Simplistcally, EPR claimed there could be no spooky action at a distance (this was the bit of entanglement they attacked) and that all the predictions of entanglement worked just as well if you had a simple locally set and valid hidden variable. Bell's Theorem provided a way to test this - but you have to be in a regime in which the distributions will be different for a local hidden variable and for a pair of qm entangled particles; thus the Aspect experiment etc which do leverage this statistical fact

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Since entanglement versus classical pairing predicts different results when the filters are at the same angle, does anyone have a reference to those experimental results? Those results will be easy to analyse.

I don't have any handy. Maybe when I'm back at work.

Thanks, seeing the results for such a straight forward experiment would be really helpful - I've only been able to find results for when the polarizing filters are at angles.

At the moment, I have a mental block on quantum entanglement being real, but on seeing the results, would accept it in preference to 'spooky action at a distance'.

Bell's test was devised to show that EPR's idea of local hidden variables was incorrect. Simple tests that show a difference between classical predictions and quantum mechanical measurements would still fall foul of EPR's claim that the results could flow from some non-classical but still locally hidden variable. What was Bell's genius was to realise that a simple statistics test can show the possibility of a set of data ie which distribution of results can theoretically be produced from a single joint distribution.

Simplistcally, EPR claimed there could be no spooky action at a distance (this was the bit of entanglement they attacked) and that all the predictions of entanglement worked just as well if you had a simple locally set and valid hidden variable. Bell's Theorem provided a way to test this - but you have to be in a regime in which the distributions will be different for a local hidden variable and for a pair of qm entangled particles; thus the Aspect experiment etc which do leverage this statistical fact

Thanks, this is starting to become clearer as to what local hidden variables means and why something was needed to discount them, i.e. Bell's inequalities.

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Since entanglement versus classical pairing predicts different results when the filters are at the same angle, does anyone have a reference to those experimental results? Those results will be easy to analyse.

Thanks, seeing the results for such a straight forward experiment would be really helpful - I've only been able to find results for when the polarizing filters are at angles.

They often will be at 90º, if the source emits photons of orthogonal polarization.

There probably aren't many papers that discuss the basics, because once it's confirmed, scientists do experiments that rely on it rather than a direct replication of the experiment. So Bell tests, for example, are a confirmation of entanglement, even though they aren't checking to see than entanglement is right. The experiment wouldn't work if it weren't true. In that regard, why wouldn't an explanation or example suffice?

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Since entanglement versus classical pairing predicts different results when the filters are at the same angle, does anyone have a reference to those experimental results? Those results will be easy to analyse. ...

I agree. Split the photons, measure both ends at 0 and 90 degrees to make sure it works, change to 45 degrees and see what correlation you get.

I think the reason you do not see this simple an experiment is that they will not behave as entangled particles ie. not all will match at 45 degrees.

Most experiments (ie. here) talk about creating an entangled state. In this one, they first linearly polarize the photon, then they cause the photon to spin by putting it through a birefringent quartz plate. The spinning photon hits the BBO splitter crystal in a random real polarization, splits and the two photons head off to the detectors to check for a match.

I dont really see why the first simple case does not produce entanglement, but yet we are to believe that the second setup with the real experiment produced entanglement. In their words "Coincidences are detected by a fast logic circuit and recorded by a personal computer" - they are only adding up the matches so this experiment can be reproduced with classical pairing or entangled particles - ie. "wobbly photons" that are a bit random when measured off their basis vectors.

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I agree. Split the photons, measure both ends at 0 and 90 degrees to make sure it works, change to 45 degrees and see what correlation you get.

I think the reason you do not see this simple an experiment is that they will not behave as entangled particles ie. not all will match at 45 degrees.

Most experiments (ie. here) talk about creating an entangled state. In this one, they first linearly polarize the photon, then they cause the photon to spin by putting it through a birefringent quartz plate. The spinning photon hits the BBO splitter crystal in a random real polarization, splits and the two photons head off to the detectors to check for a match.

I dont really see why the first simple case does not produce entanglement, but yet we are to believe that the second setup with the real experiment produced entanglement. In their words "Coincidences are detected by a fast logic circuit and recorded by a personal computer" - they are only adding up the matches so this experiment can be reproduced with classical pairing or entangled particles - ie. "wobbly photons" that are a bit random when measured off their basis vectors.

What do you mean by first simple case?

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First simple case: Split the photons, measure both ends at 0 and 90 degrees to make sure it works, change to 45 degrees and see what correlation you get.

I mean a very straight forward vertically polarized stream of photons. When split, all should match at 0 and 90 degrees, how many match when both ends measure at 45 degrees. Are they normal pairs, or are they entangled?

Edited by edguy99
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First simple case: Split the photons, measure both ends at 0 and 90 degrees to make sure it works, change to 45 degrees and see what correlation you get.

I mean a very straight forward vertically polarized stream of photons. When split, all should match at 0 and 90 degrees, how many match when both ends measure at 45 degrees. Are they normal pairs, or are they entangled?

How do you "split" the photons?

The way it's done for entanglement is crucial to that working. You can't tell which one is which, and that's why its wave function is entangled.

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In the article linked "Our BBO crystals are cut for Type I phase matching, which means that the signal and idler photons emerge with the same polarization, which is orthogonal to that of the pump photon."

Notice they start out with a linear beam:

"To create the state |ψEPRi or something close to it, we adjust the parameters which determine the laser polarization. First we adjust θl to equalize the coincidence counts N(0◦ , 0 ◦ ) and N(90◦ , 90◦ )."

At this point, N(45◦ , 45◦ ) is way to low. They then cause the beam to spin so all paired input angles equalize:

"Next we set φl by rotating the quartz plate about a vertical axis to maximize N(45◦ , 45◦ )."

I like talking about this experiment because it has a lot of detail. If you have another specific example of how they achieve entanglement, it would be great to take a look at a few others.

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The detail of why spontaneous parametric downconversion yields entangled pairs is lacking. It's crucial that you can't tell the photons apart. Maximizing the 45 degree signal, AFAICT means your vertical and horizontal probabilities are equal - you don't know the polarization ahead of time, another crucial aspect.

They then cause the beam to spin so all paired input angles equalize:

That's a phase shift, not a "spin"

---

You still haven't explained how you would "split" photons for the "simple" case

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Just saw the new star wars movie in 3D and was wearing the glasses with spin left over one eye and spin right over the other eye. The spin (rotation of the electrical axis) is indeed caused by a phase shift.

WRT explaining how photons are split, it is the same for the simple and the complex case. I tried to stick to the article's wording of the action of the BBO crystal "that the signal and idler photons emerge with the same polarization, which is orthogonal to that of the pump photon".

What I find interesting here, is the "simple" case of shooting linearly polarized photons directly at the splitter does not cause the split photons to be entangled. Yet the more "complex" case of shooting linearly polarized photons first through a birefringent quartz plate to phase shift the photons (cause spin) before shooting them at the splitter results in entangled photons (as long as you throw out all the mis-matched photons).

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Just saw the new star wars movie in 3D and was wearing the glasses with spin left over one eye and spin right over the other eye. The spin (rotation of the electrical axis) is indeed caused by a phase shift.

Photons are spin 1. The description you should use is circular polarization.

WRT explaining how photons are split, it is the same for the simple and the complex case. I tried to stick to the article's wording of the action of the BBO crystal "that the signal and idler photons emerge with the same polarization, which is orthogonal to that of the pump photon".

What I find interesting here, is the "simple" case of shooting linearly polarized photons directly at the splitter does not cause the split photons to be entangled. Yet the more "complex" case of shooting linearly polarized photons first through a birefringent quartz plate to phase shift the photons (cause spin) before shooting them at the splitter results in entangled photons (as long as you throw out all the mis-matched photons).

Because to entangle the photons you can't have knowledge of their states. If you send linearly polarized light into the BBO crystal, you get two photons of the orthogonal polarization out. You know what the state is without having to do a measurement. But circularly polarized light is a superposition of the two linear polarizations, and since you have two crystals orthogonal to one another, you can get either polarization out, depending on which crystal does the downconversion. As long as you can't tell, you have the conditions for entanglement.

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...

Because to entangle the photons you can't have knowledge of their states. If you send linearly polarized light into the BBO crystal, you get two photons of the orthogonal polarization out. You know what the state is without having to do a measurement. But circularly polarized light is a superposition of the two linear polarizations, and since you have two crystals orthogonal to one another, you can get either polarization out, depending on which crystal does the downconversion. As long as you can't tell, you have the conditions for entanglement.

So I am correct in thinking that if you can possibly know what the state is without measurement (and thus disruption of the state) then you cannot have entanglement? Ie it is that strict

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So I am correct in thinking that if you can possibly know what the state is without measurement (and thus disruption of the state) then you cannot have entanglement? Ie it is that strict

So far as I know, yes. In a way it isn't strict, because e.g. just obscuring the origin of particles (combining them using a beamsplitter) can entangle them, if you do it right. Any random particle you detect is probably entangled with countless others. The strictness is in entangling in a useful way for an experiment. Having an entangled particle but not its partner is not very useful.

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Photons are spin 1. The description you should use is circular polarization

Yes, spin 1 with 3 states, left-spin, right-spin and linear. Words can sometimes cause confusion - to me, polarization is the Jones Vector, but of course the position of the Jones Vector is only a probability that the orientation is really that direction. This is a useful chart to help with the relationship between visual demos, Jones Vectors and Bra-ket notation.

Because to entangle the photons you can't have knowledge of their states. If you send linearly polarized light into the BBO crystal, you get two photons of the orthogonal polarization out. You know what the state is without having to do a measurement. But circularly polarized light is a superposition of the two linear polarizations, and since you have two crystals orthogonal to one another, you can get either polarization out, depending on which crystal does the downconversion. As long as you can't tell, you have the conditions for entanglement.

Very well worded, +1

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