PDC Type I: Unreasonable "Elements of Reality" in Bell Tests?

[DrChinese]

EPR defined a form of realism which later figured in Bell's Theorem. If the outcome of a particle's observation could be predicted with certainty, then the observable had an "element of reality". In Bell tests, that is usually given as photon polarization. We see the so-called "perfect" correlations in which Alice and Bob, when observed at the same polarization angle, always give perfectly correlated (or anticorrelated) results at any given angle.

The normal method of getting these results is to use PDC crystals, either Type I or Type II. Type II crystals yield anti-correlated photon pairs, while Type I yield correlated pairs. There is an interesting wrinkle in Type I pair generation, and this is what I have questions about.

It takes 2 perpendicularly oriented Type I crystals to yield a polarization entangled stream of photon pairs. A single Type I crystal provides an output stream of known polarization, perpendicular to the input source. This stream, by itself, does not yield perfect correlations that would match the EPR definition of having an element of reality at any chosen observation angle.

When the input stream is V>, The output stream is H>H> which does not lead to perfect correlations. If the crystal is rotated 90 degrees: the input stream is now H>, The output stream is V>V> which still does not lead to perfect correlations. If there are 2 perpendicularly aligned crystals whose streams are mixed suitably, we end up with a superposition of H>H> + V>V>, which is a good Bell state and the perfect correlations appear. This is how Type I crystals are used in actual Bell tests.

So it seems to me that what we have here is 1+1=3. Suppose we had 2 completely independent lasers driving 2 completely separate - but perpendicular - Type I PDC crystals. The pair output of these setups would individually not be in Bell states (i.e. no perfect correlations). But if there are suitably combined in such a way that the source apparatus cannot, in principle, be determined, then the combined beam becomes a good Bell state. And it now passes the EPR "element of reality" test. Yet, clearly the photon pair came from one or the other of the two crystals, which did NOT pass the "element of reality test" individually. So the photon pair must have picked up "something" from the presence of the other crystal, even though nothing came from there. That's unreasonable!

My conclusion is that "elements of reality", if they exist, are unreasonable. Am I crazy? I guess what I am saying is that any mechanistic picture of what is going on will always fail, even though the formalism works fine.

-DrC

 

[RandallB]

The normal method of getting these results is to use PDC crystals, either Type I or Type II. Type II crystals yield anti-correlated photon pairs, while Type I yield correlated pairs. There is an interesting wrinkle in Type I pair generation, and this is what I have questions about.

It takes 2 perpendicularly oriented Type I crystals to yield a polarization entangled stream of photon pairs. A single Type I crystal provides an output stream of known polarization, perpendicular to the input source. This stream, by itself, does not yield perfect correlations that would match the EPR definition of having an element of reality at any chosen observation angle.

When the input stream is V>, The output stream is H>H> which does not lead to perfect correlations. If the crystal is rotated 90 degrees: the input stream is now H>, The output stream is V>V> which still does not lead to perfect correlations. If there are 2 perpendicularly aligned crystals whose streams are mixed suitably, we end up with a superposition of H>H> + V>V>, which is a good Bell state and the perfect correlations appear. This is how Type I crystals are used in actual Bell tests.

Do you have a link or source that details a bit about how Type I PDC need to be fabricated I did not know it required two crystals to make them useful.

The mostly I want to be sure I’m understanding how the Type one crystal works. If one produces paired photons but the fail to retain “entanglement” characteristics. But putting two in series allows one to down convert V inputs and the other H inputs each must be having some effect on the down converting photons produced by the other in order to gain the “entanglement” characteristics lost when only one was used. Do they explain any requirement to avoid any gap between the two crystals or can they be stacked with some distance between them. Any reference that gives some more detail on how the Down-converters need to be fabricated would be helpful.

As to separating the two required Type I crystals into two separate source beams – I’d assume that both are required by each photon to build the full “entanglement” characteristics -- so the approach your suggesting should not work. That is gaining the “entanglement” part is a 1+1 = 2 crystals required in a beam to work.

 

[DrChinese]

Here is an article that has some additional detail about Type I PDC:

Dietrich Dehlinger and M. W. Mitchell: Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory (PDF), American Journal of Physics, 2002.

See Section V. (Polarizations) and Figure 2.

 

[RandallB]

Interesting. I wonder if someone has documented the correlation failure results of using just on crystal. I’m wondering if it tracked with the Classical 25% to 75% probabilities at the limits, Or if it tracked with the Bell limits of a straight line 100% to 0% ie. failing to cross that line.

I was under the impression that the type II DC not only required two crystals, but need an optimal non-orthogonal alignment wrt pump beam for the separating cones of light to overlap usefully.

I’ll have to look for more on how SPDC units are put together.

DrC, did you understand my comment on "1+1 = 2 crystals" may be required to build a “good Bell state” so that the individual photons actually go through both crystals?

 

[DrChinese]

DrC, did you understand my comment on "1+1 = 2 crystals" may be required to build a “good Bell state” so that the individual photons actually go through both crystals?

Well, they go through both crystals but only one physically acts on each photon/pair. Just as with the double slit, the possibility of going through either slit gives rise to the interference pattern... with the 2 crystals you get entanglement.

I cannot say for an absolute fact that you could build the Bell state from combining 2 separate source lasers and separate crystals... but I assume it is possible to create such a superposition. Anyone out there know more?

 

[RandallB]

Well, they go through both crystals but only one physically acts on each photon/pair. Just as with the double slit, the possibility of going through either slit gives rise to the interference pattern... with the 2 crystals you get entanglement.

NO I disagree;
In the double slit we are forced to consider that possibility of using both.
Both with the 2 crystals there is no chance of any photon not being under the influence of both crystals. If the 1st one causes the down conversion both photons a must go though the 2nd subjecting them to some unseen adjustments. But if the 2nd one causes the down conversion it cannot have received the one photon without it having gone through the 1st where it could be subjected to some unseen preparation before down conversion.
Those would be local and realistic effects not the same as a non-local second slit. Hence my 1+1 = 2 crystals required.

I must say it is a little disappointing not to be able to find more data on exactly how tests on one crystal do not produce Bell volitions. It would be nice to know which of the Local-Realistic interpretations it matched best, the inequity line or the 75% to 24% line.

 

[DrChinese]

As far as anyone knows, the presence of a second Type I crystal does not affect the down converted output photons (or the source input photon). The crystals send the output photons "off angle" in cones. They are collected in areas in which the output cones overlap sufficiently that the source crystal cannot be determined. This combination leads to the H>H> + V>V> superposition, and thus the Bell state.

There is nothing - from a QM perspective - needed to explain this result in the way of some interaction between the 2 crystals. But I do think there is a problem explaining what happens from a deterministic perspective. I.e. if you accept Bohmian/dBB explanations, you do need there to be something "extra" going on because there is no entanglement from either one individually, and yet this stream purports to be deterministically splitting at either one or the other of the crystals.

Type II crystals, on the other hand, work very similarly but do not rely upon a superposition of 2 output streams to get a Bell state. They send out H>V> + V>H> directly, which is entangled.

 

[RandallB]

You are missing the point.
Example: Using one beam with a HH crystal in the first position you can select two beams and get HH but there is no “entanglement”.
Likewise with only the second slot filled with a VV crystal. The same two beams selection gives VV output one V in each beam but again you are reporting no measurable entanglement is observed.

But you are reporting entanglement when both HH and VV are outputted by using both crystals.
You also know the change cannot be due to any H reacting to a V because they never come through together by design of the experiment.
But to you did change how the photons were prepared before detection and the change was a local one. The pair of HH photon was prepared with additional filtering through a VV crystal after DC.
And the VV pump photon was pre-filtered by a HH crystal before DC.
You cannot even claim it something like the Moon is not really there until I see or measure it somehow. Because you did observe the action of the added filter, with no entanglement observation before changing to entanglement observed after adding the extra filtration.
From a QM perspective – Copenhagen requires the preparations be well accounted for; obviously the QM formula would reduce to 1+0 crystal = no entangle vs 1+1 = entangle.

I don’t understand your Type II comments – the diagram on your own web pages show 2 output streams.

 

[ueit]

When the input stream is V>, The output stream is H>H> which does not lead to perfect correlations. If the crystal is rotated 90 degrees: the input stream is now H>, The output stream is V>V> which still does not lead to perfect correlations. If there are 2 perpendicularly aligned crystals whose streams are mixed suitably, we end up with a superposition of H>H> + V>V>, which is a good Bell state and the perfect correlations appear. This is how Type I crystals are used in actual Bell tests.

So it seems to me that what we have here is 1+1=3. Suppose we had 2 completely independent lasers driving 2 completely separate - but perpendicular - Type I PDC crystals. The pair output of these setups would individually not be in Bell states (i.e. no perfect correlations). But if there are suitably combined in such a way that the source apparatus cannot, in principle, be determined, then the combined beam becomes a good Bell state. And it now passes the EPR "element of reality" test. Yet, clearly the photon pair came from one or the other of the two crystals, which did NOT pass the "element of reality test" individually. So the photon pair must have picked up "something" from the presence of the other crystal, even though nothing came from there. That's unreasonable!

1. I don't understand why an "element of reality test" requires entangled photons. If the output photons are not correlated (entangled) that means that some angular momentum has been transferred to other particles in the crystal. The conservation laws require that. If you could measure the spin of all particles in the crystal + one of the emitted photons you could certainly predict the spin of the other photon, so it is "real".

2. You say that nothing came from the other crystal. This cannot be true because that crystal contains charged particles. And charged particles produce a field. The field of a single crystal is different from the field produced by two crystals. Nothing unreasonable about that. One planet goes straight. Another one goes the same. Both of them go round and round. Is this another case when 1+1=3?

My conclusion is that "elements of reality", if they exist, are unreasonable. Am I crazy? I guess what I am saying is that any mechanistic picture of what is going on will always fail, even though the formalism works fine.

I think that by "mechanistic picture" you understand only billiard balls going straight and bumping into each other. Did you consider the hypothesis that each quantum particle can be accompanied by a classical-like local field and therefore interact with other particles without a direct collision?

 

[DrChinese]

1. I don't understand why an "element of reality test" requires entangled photons. If the output photons are not correlated (entangled) that means that some angular momentum has been transferred to other particles in the crystal. The conservation laws require that. If you could measure the spin of all particles in the crystal + one of the emitted photons you could certainly predict the spin of the other photon, so it is "real".

2. You say that nothing came from the other crystal. This cannot be true because that crystal contains charged particles. And charged particles produce a field. The field of a single crystal is different from the field produced by two crystals. Nothing unreasonable about that. One planet goes straight. Another one goes the same. Both of them go round and round. Is this another case when 1+1=3?



I think that by "mechanistic picture" you understand only billiard balls going straight and bumping into each other. Did you consider the hypothesis that each quantum particle can be accompanied by a classical-like local field and therefore interact with other particles without a direct collision?

I am not sure that an "element of reality" test requires entangled photons. EPR states that if the result of an observation can be predicted with certainty, there is an element of reality to that which is observed. Clearly, entangled photons can be used to create such a scenario.

As to the field produced by 2 crystals: essentially, I am saying that the 2nd crystal produces no tangible effect. Of course it produces something, but so does air and that does not create a Bell state. I think the effect can be demonstrated without 2 crystals in series, but I am not certain about that.

 

[ueit]

I am not sure that an "element of reality" test requires entangled photons. EPR states that if the result of an observation can be predicted with certainty, there is an element of reality to that which is observed. Clearly, entangled photons can be used to create such a scenario.

You could, in principle, predict the spin of a photon comming from a light bulb by measuring the spin of the atom before and after the emission. So, the spin of any photon is as "real" as the spin of an entangled one. This experiment is, however, experimentally unfeasible.

As to the field produced by 2 crystals: essentially, I am saying that the 2nd crystal produces no tangible effect.

1. It certainly produces a "tangible effect" because the experimental result shows that. So, it is not a question of "if" but of "how". The most probable answer is IMHO that the particles inside both crystals produce a field that influences the emission process.

Of course it produces something, but so does air and that does not create a Bell state. I think the effect can be demonstrated without 2 crystals in series, but I am not certain about that.

The air should, indeed, influence the emission but because the motion of air molecules is random, this effect is indistinguishable from noise.

 

[DrChinese]

You could, in principle, predict the spin of a photon coming from a light bulb by measuring the spin of the atom before and after the emission. So, the spin of any photon is as "real" as the spin of an entangled one.

That was essentially the EPR argument, they did not know that Bell states existed at the time. Quite the opposite, they assumed that the Heisenberg Uncertainty Principle was incomplete.

At any rate, here is a question:

Take a laser source, run it through a Polarizing Beam Splitter (PBS) so we have 2 separate output streams, H> and V>. Take the H> stream into a PDC crystal and get V>V> out, and take the V> stream into a second PDC crystal and get H>H> out. Now, recombine the 4 output streams so that you end up with 2 streams which will now be H>H> + V>V>. This is done in such a way that the path taken cannot, in principle, be determined.

Will the resulting output streams be entangled in a Bell state? I am saying it will, and that the 2 crystals do NOT need to be in series to create a Bell state.

 

[RandallB]

As to the field produced by 2 crystals: essentially, I am saying that the 2nd crystal produces no tangible effect.

I don't understand how you can claim that. It can only be an unfounded assumption what can support it?
Your own observations contradict it.
You shown us that same total number of photons produced by the two crystals separately are still produced when used together. But when used together they produce an observable change when you measure them - entanglement. You do consider entanglement a tangible observation right - and the only local change that could be causal is the inline second crystal. (I.E. 2 crystals DO NEED to be in series to create a Bell state).

Also, from earlier you said:
“When the input stream is V>, The output stream is H>H> which does not lead to perfect correlations. If the crystal is rotated 90 degrees: the input stream is now H>, The output stream is V>V> which still does not lead to perfect correlations.”

The comment (the input stream is now H>,) is incorrect - rotating the crystal does not change the input stream alignment only the alignment of the crystal wrt it. There is no evidence a crystal is sensitive to the polarization of the input stream, in fact the paper you provided in post #3 shows a polarizer in the source beam (fig 1); yet both crystals do their job the same. The only thing controlling the output alignment is the crystal not the input stream. The results give no indication as to what the alignment of a Pump Beam photon may have been.

I also found something I’d not seen before:
http://www.redoptronics.com/BBO-cut.html
Table 1. there shows both a type I & II UP CONVERSION (?) of 1064nm to 355nm using a Third Harmonic .
That is three photons becoming one!

Yikes; how does a BBO do that?

 

[DrChinese]

Also, from earlier you said:
“When the input stream is V>, The output stream is H>H> which does not lead to perfect correlations. If the crystal is rotated 90 degrees: the input stream is now H>, The output stream is V>V> which still does not lead to perfect correlations.”

The comment (the input stream is now H>,) is incorrect - rotating the crystal does not change the input stream alignment only the alignment of the crystal wrt it. There is no evidence a crystal is sensitive to the polarization of the input stream, ...

The crystals are definitely sensitive to the polarization of the input stream. Only 1 polarization (either H> or V> depending on orientation) is supported by Type I crystals. That is why you need 2 oriented orthogonally to get a Bell state. Usually the pump input laser is oriented at a 45 degree angle so that half of the input is H> and half is V> (randomly). So half acts within one crystal, half in the other.

 

[RandallB]

The crystals are definitely sensitive to the polarization of the input stream. Only 1 polarization (either H> or V> depending on orientation) is supported by Type I crystals. That is why you need 2 oriented orthogonally to get a Bell state. Usually the pump input laser is oriented at a 45 degree angle so that half of the input is H> and half is V> (randomly). So half acts within one crystal, half in the other.

Ok I can accept that;
but it still only says that the V photons are not converted by a H crystal.
That does not mean the H crystal cannot modify V photons in a way that can only be detected by a V crystal producing “entangled” photon pairs it could not otherwise produce.
The observations you’re pointing out supports that the H crystal do modify V photons that way and therefore; 2 crystals DO NEED to be in series to create a Bell state.

 

[ueit]

That was essentially the EPR argument, they did not know that Bell states existed at the time. Quite the opposite, they assumed that the Heisenberg Uncertainty Principle was incomplete.

Bell states are not different in this aspect. It is just momentum conservation, which always holds. You can always predict the spin on a certain axis in the way I said. In order to see a problem for realism you need a supplementary assumption, that the spin of the entangled particles, on any axis, remains the same regardless of how you measure it. This assumption only makes sense in a naive, billiard-ball interpretation. Even for a classical field theory such an assumption is wrong. The trajectory of a particle depends of the configuration of other particles around it.

At any rate, here is a question:

Take a laser source, run it through a Polarizing Beam Splitter (PBS) so we have 2 separate output streams, H> and V>. Take the H> stream into a PDC crystal and get V>V> out, and take the V> stream into a second PDC crystal and get H>H> out. Now, recombine the 4 output streams so that you end up with 2 streams which will now be H>H> + V>V>. This is done in such a way that the path taken cannot, in principle, be determined.

Will the resulting output streams be entangled in a Bell state? I am saying it will, and that the 2 crystals do NOT need to be in series to create a Bell state.

You are probably right. But how does this new setup affect my argument? You still have different matter configurations leading to different experimental results.

 

[DrChinese]

You are probably right. But how does this new setup affect my argument? You still have different matter configurations leading to different experimental results.

Sorry, in the exchange I lost the sense of what you are asserting. I don't dispute that there are a variety of ways of express entanglement and/or conversation laws besides PDC photon pairs. But they produce Bell states that have 2 important properties: they display the "perfect" correlations when measured at identical settings, and they violate Bell inequalities at specificied other settings.

On the other had, the individual streams of Type I PDC crystals show neither of these qualities. yet when 2 output streams are combined, each photon pair emerging individually gains the Bell state attributes. Now, how can a mechanical explanation provide an answer in this case? I say that the QM formalism does precisely because it is *silent* on the mechanics and does not insist on "realism". On the other hand, any realistic explanation - even non-local ones - are going to have a severe problem here. I would propose that any non-local mechanical hypothesis be required to explain this Type I PDC paradox satisfactorily without resorting to the familiar "My theory always gives the same answers as QM" mantra.

Once again, the paradox is: A single particle pair emerges in a Bell state ONLY when the output of 2 PDC crystals are combined, even though that same particle pair must emerge from the source PDC crystal *without* being a Bell state. The presence of the 2nd crystal, from which the pair could not have emerged, does nonetheless figure into the emergence of the Bell state. In a deterministic theory (as BM/dBB claims to be, for example), it must have gone through one or the other and not a superposition of both. So I say that BM/dBB cannot truly claim to be a deterministic theory and still provide an adequate explanation of this paradox.

 

[RandallB]

PDC Type I: 2 together or separate & combined

On the other had, the individual streams of Type I PDC crystals show neither of these qualities. yet when 2 output streams are combined, each photon pair emerging individually gains the Bell state attributes. Now, how can a mechanical explanation provide an answer in this case? I say that the QM formalism does precisely because it is *silent* on the mechanics and does not insist on "realism". On the other hand, any realistic explanation - even non-local ones - are going to have a severe problem here. I would propose that any non-local mechanical hypothesis be required to explain this Type I PDC paradox satisfactorily without resorting to the familiar "My theory always gives the same answers as QM" mantra.

Once again, the paradox is: A single particle pair emerges in a Bell state ONLY when the output of 2 PDC crystals are combined, even though that same particle pair must emerge from the source PDC crystal *without* being a Bell state. The presence of the 2nd crystal, from which the pair could not have emerged, does nonetheless figure into the emergence of the Bell state. In a deterministic theory (as BM/dBB claims to be, for example), it must have gone through one or the other and not a superposition of both. So I say that BM/dBB cannot truly claim to be a deterministic theory and still provide an adequate explanation of this paradox.

I disagree with ueit; I still think you are probably wrong.
First on the point made:
“On the other hand, the individual streams of Type I PDC crystals show neither of these qualities.”

Exactly what plot is produced by using a single Type I PDC crystal; let's say where A is held to a measurement at 45°. What would the observed plot at B from 0° to 90° show, do we have anything where someone has published actual observations for something like that?

Second: A
“Bell state ONLY when the output of 2 PDC crystals are combined”
Is not what is happening. Experiments that show the Bell State do not “combine” outputs – the outputs are overlapping there is a difference. Your set up is the plan that requires combining separate beams for two separate crystals not stacked.

SO
“Now, how can a mechanical explanation provide an answer in this case?”
Easy and I already have.
Neither of the independently created but overlapping beams can avoid going though the crystal that not responsible its down conversion at some local point either before or after the DC. Therefore the experiment does not eliminate the possibility of some unknown hidden local[/] influence on the individual photon parameters as they pass through the other crystal.

Your modified test (do we know if anyone has actually thought to try it) does remove the possibility of any individual photon from being modified by both crystals. Since yours would eliminate any chance of some hidden local influence I predict such a test would fail to produce Bell correlations by combining the two beams.

So the question is – if your set up did fail to produce a Bell State – would that be seen as support for some realistic local influence?

Unless an experimenter though it would, there is probably little point in doing the experiment.
I doubt there would be much interest in trying it – I suspect QM experts would say even QM expects the, two beam split and then combined, plan would fail to produce a Bell State.

 

[DrChinese]

“On the other hand, the individual streams of Type I PDC crystals show neither of these qualities.”

1. Exactly what plot is produced by using a single Type I PDC crystal; let's say where A is held to a measurement at 45°. What would the observed plot at B from 0° to 90° show, do we have anything where someone has published actual observations for something like that?

2. Second: A
“Bell state ONLY when the output of 2 PDC crystals are combined”
Is not what is happening. Experiments that show the Bell State do not “combine” outputs – the outputs are overlapping there is a difference. Your set up is the plan that requires combining separate beams for two separate crystals not stacked.

1. With 1 crystal of Type I, the output polarization is known. If the input was oriented to H>, then the output is V>V>. This is not an entangled state, so you won't see the perfect correlations except at the known spots: V> or H>. I think the general formula is:

C = (cos^2(A) * cos^2(B)) + (sin^2(A) * sin^2(B))

This is the same formula as any 2 vertically aligned photons, having no other connection. Unlike with entangled photons, this does not reduce to a formula which has theta as the only variable.2. Yes, the 2 cones overlap (one cone for each crystal). But the overlapping cones do make for the combination of the output stream, and it is done somewhat for convenience. It makes it easier to collect and merge the streams into a single stream. Here is a quote from the authors (actually from a companion piece - emphasis added):

"A given crystal can only support Type I downconversion
of one pump polarization, the other polarization
simply passes through the transparent crystal. Our source uses
two identical crystals, with one rotated 90◦ from the other
about the beam propagation direction, as shown in Figure 2.
In this arrangement each crystal can support downconversion
of one pump polariazation. A 45◦ polarized pump photon
can downconvert in either crystal, producing a polarization entangled
pair of photons"

 

[RandallB]

C = (cos^2(A) * cos^2(B)) + (sin^2(A) * sin^2(B))

That doesn’t make sense! Given two correlated beams with only VV and holding A @ 45°. Wouldn’t this give a plot of correlations with B going from 0 to 90° of 50% at all angles. There shouldn’t be any photons detected at 90° by B.
More important, What has actually been measured for real!

the other polarization simply passes through the transparent crystal.

Yes I understand that is what is claimed – that’s the whole point.
What is offered as proof no hidden effect is happening as they simply passes through the other transparent crystal?
Do you think your set up might give that proof?
1.) What do you think the meaning would be if you do build a Bell State by combining four beams into 2.
AND
2) What do you think it would mean if your set up fails to produce a Bell State by combining four beams into 2.

Would that failure mean that when photons simply passes through the other transparent crystal something local but unknown must be happening we are not aware of, that contributes to building the Bell State?

 

[DrChinese]

1. That doesn’t make sense! Given two correlated beams with only VV and holding A @ 45°. Wouldn’t this give a plot of correlations with B going from 0 to 90° of 50% at all angles. There shouldn’t be any photons detected at 90° by B.


2. Would that failure mean that when photons simply passes through the other transparent crystal something local but unknown must be happening we are not aware of, that contributes to building the Bell State?

1. I should have made clear:

C = (cos^2(A) * cos^2(B)) + (sin^2(A) * sin^2(B))

where C represents the correlations, either both detected as V or both detected as H.


2. I think if there was something added by the second crystal, that would have been noticed years ago. The Type II PDC crystals produce an entangled state using just one crystal, the reason being that the output varies between H>V> and V>H> when a 45 degree pump input stream is applied. The Type I crystals produce a single polarization, so they can do that. So I don't think there is much likelihood of there being something missed. But my proposed setup might make that more clear.

 

[RandallB]

1. I should have made clear:

C = (cos^2(A) * cos^2(B)) + (sin^2(A) * sin^2(B))
where C represents the correlations, either both detected as V or both detected as H.

So to be clear for a single crystal are you claiming?
C = (cos^2(A) * cos^2(B))
Somehow that does not seem right, but what counts are actual observations. I’m assuming someone has, what I’ve not found is where such observations of correlations using a single crystal have been published.

2. I think if there was something added by the second crystal, that would have been noticed years ago.

But we have noticed for years that the Bell State is addded! It only appears when there is the opportunity for “something added” by a second crystal in close enough alignment to cause overlapping. I’ve seen nothing to make clear that is not the case.

But my proposed setup might make that more clear.

Maybe; If so, it could be a very important experiment and from what I see easily within the capabilities of an undergraduate program as described it the paper you have referenced. But before having someone actually do even a relatively easy one (as quantum tests go), there hould be a clear statement as to the meaning of each of the two possible outcomes (Bell State or No Bell State) of the experiment as I asked.
Do you have an idea of what you would conclude if the results were not as you hope and no Bell State was found? Would you only accept reality as "local"? If not what's the point in doing the test?

I would think a physics program able to do such a test such as University of Texas at Austin or University of Illinois at Urbana-Champaign would most value doing experiments where different outcomes will support different conclusions about existing assumptions.

Personally, I would love to stake our differences on the outcome of your proposed experimental setup with no option to change our minds if the experiment does not go my way. Bell State produced as you propose - Non-Local Reality confirmed - and I’ll never question it again. Or Bell State not produced - Local Reality confirmed - and you never dispute it again.

But as a Local Realist I feel I’d be taking advantage;
Because I’m convinced the real experts in Texas and Illinois would use QM, prior to running the experiment, to predict No Bell State for your experiment. And I think they would even add that if your experiment did produce a Bell State they would, in advance of seeing such a result, state that it would mean either a serious problem with how QM is defined or that something was wrong with the way the test was preformed.

Of course if you check with the experts and I’m right about what they would predict -- it kind of knocks the wind out of any need to do the experiment since QM & LR predict the same thing.

The Type II PDC crystals produce an entangled state using just one crystal,

Are you sure about that? I know polarizing beam splitters are not just one prism but two joined together. I was under the impression that some (maybe all) Type II PDC devices were also made of two special cut crystals joined and aligned at a certain angle wrt the incoming beam to get the two output cones to overlap as needed. I’m not sure how to confirm the actual fabrication of a Type II PDC.

 

[DrChinese]

So to be clear for a single crystal are you claiming?
C = (cos^2(A) * cos^2(B))
Somehow that does not seem right, but what counts are actual observations. I’m assuming someone has, what I’ve not found is where such observations of correlations using a single crystal have been published.

The term you provided is only for the H>H> match. The sin^2 term is for the V>V> match as well. You add them to get the total correlations (matches). The reason you haven't seen it published anywhere is that the result doesn't add to our knowledge in any way. The output of a single Type I PDC crystal is not entangled and that is the interesting side of things. I am sure that experimenters have noted this result many times as they perform alignment and other tests as part of a "normal" Bell test using 2 crystals.

On the other hand: The proposed setup does *not* test local reality. It is just a way to highlight the difficulty with mechanistic explanations. QM says, in effect, 1+1=3. But a mechanical explanation - one which purports to describe what is going on in physical (and not just mathematical) terms - will have problems with this treatment.

 

[DrChinese]

Attached is a diagram of the proposed setup. In this setup, the Type I PDC crystals are in parallel rather than their normal series alignment.

I realize it might be difficult to achieve this arrangement in practice, as the paths must be precisely setup so that the path taken cannot be determined. Care must be taken that there is no destructive interference as well.

 

[DrChinese]

Here is another copy of the diagram in case you can't read the one from the previous post:

Bel state from 2 Type I PDC crystals in parallel

 

[RandallB]

The term you provided is only for the H>H> match. The sin^2 term is for the V>V> match as well. You add them to get the total correlations (matches). The reason you haven't seen it published anywhere is that the result doesn't add to our knowledge in any way.

I don’t understand what you are saying, we were taking about the correlation plots of a single crystal producing paired photons: a H> stream going to Alice and a H> stream going to Bob. When testing that simple set up how would the V outputs be involved?

On the other hand: The proposed setup does *not* test local reality. It is just a way to highlight the difficulty with mechanistic explanations. QM says, in effect, 1+1=3.

I do not understand what you mean by “QM says 1+1=3”. Are you saying you believe the set up you have diagramed would be clearly have a pre-experiment prediction made by QM as showing a Bell State?
(PS I had understood "seperate & combined" to mean exactly what you have diagramed)

I’m not asking what you think the experiment will show, I’m asking what you think the QM formalism as currently defined claims the results should be. Bell State or No Bell State?

If you do think QM actually does predict your set up will produce a Bell State then I disagree; you do have a test of Local verses at least an interpretation of QM! An interpretation that would need to be revised and corrected when the experiment fails.

As I’ve already said - I think QM says NO Bell State for your system -- specifically because the uncertainty of the “extra” crystal in series for each photon has been removed from the system.

One extra point on your diagramed experiment:
I would give the experimenter permission to independently adjust the pump beams alignments to each crystal at their discretion by up to at least up to + or - 45°; in attempts to build a Bell State observation. Which I believe they will not be able to observe.

 

[DrChinese]

1. I don’t understand what you are saying, we were taking about the correlation plots of a single crystal producing paired photons: a H> stream going to Alice and a H> stream going to Bob. When testing that simple set up how would the V outputs be involved?

2. I do not understand what you mean by “QM says 1+1=3”. Are you saying you believe the set up you have diagramed would be clearly have a pre-experiment prediction made by QM as showing a Bell State?

1. The detector mechanism for Alice (and identically for Bob) is usually 2 detectors with a polarizing beam splitter (PBS) in front. That separates the output stream into an H> component and a V> component. The PBS can be oriented at any angle. The orientation for Alice and Bob can be varied as desired.

The output from a single Type I crystal is not entangled, so the results (correlations or matches) vary according to the settings for Alice and Bob. But since there are not "perfect" correlations", the angle between (theta) is not the only variable.

2. I am not trying to postulate anything different that what normal QM would predict. As I understand how Type I PDC works, the diagram should produce entangled photon pairs that will exhibit "perfect" correlations. I am saying that the crystals can be in series or in parallel, and that the results will be the same as long as the path taken cannot be determined.

Assuming that to be the case, I say that any realistic hypothesis will fall victim to the fact that the photon pair emerged from either one crystal or the other. However, neither crystal *individually* is capable of producing entangled photon pairs.

 

[RandallB]

1. With 1 crystal of Type I, the output polarization is known. If the input was oriented to H>, then the output is V>V>. This is not an entangled state, so you won't see the perfect correlations except at the known spots: V> or H>. I think the general formula is:

C = (cos^2(A) * cos^2(B)) + (sin^2(A) * sin^2(B))

OK this just has to be me doing something wrong in how I see what "C" means here.
I’m still not seeing how this formula can apply to a single crystal.

You are giving “C” as a correlation count formula for just a single Type I crystal.
In this example you’ve indentified one with V>V> outputs (does not matter what the pump beam is we know we have two outputs both vertical).
Meaning both Alice and Bob making simple polarization intensity measurements on the one beam they each receive with 0° defined as V> Vertical they will measure polarized light following Cos² rule. (If they had observed it following a Sin ² pattern they would call it H polarized light.) Does not matter how they measure the intensity (photon counts over a time interval is just one way).

But to make correlations measurements they must count and compare photon by photon.
I can see that at 0° measurements made by both Alice and Bob on their share of the output from a single crystal, based on Cos² 0°; gives 1 times 1 for 100% “C” correlations. I have no problem there.

But what does this formula say about “C” when both Alice and Bob are measuring at 90° ??
And exactly what photons are Alice and Bob counting as coming from this single crystal?

 

[RandallB]

2. I am not trying to postulate anything different that what normal QM would predict. As I understand how Type I PDC works, the diagram should produce entangled photon pairs that will exhibit "perfect" correlations. I am saying that the crystals can be in series or in parallel, and that the results will be the same as long as the path taken cannot be determined.

Assuming that to be the case, I say that any realistic hypothesis will fall victim to the fact that the photon pair emerged from either one crystal or the other. However, neither crystal *individually* is capable of producing entangled photon pairs.

Before trying to apply a realistic approach I noticed your diagram is not quite what you had proposed in the OP.

There you said:
“Suppose we had 2 completely independent lasers driving 2 completely separate - but perpendicular - Type I PDC crystals.”

You have changed the set up to one laser as a single source of photons using a polarizing beam splitter. Why the change? And would QM formalism and formulas evaluate the two experimental systems (one laser vs. two lasers) differently.

Also in your diagram we can assume Alice and Bob will use a Polarizing beam splitter with a pair of detectors as their measuring device to collect maximum information.
But will your set up allow them to use two measuring devices each so the can measure the two beams V> & H> delivered to them independently and simply combine the detection counts before correlating between Alice & Bob.

So, in order to apply QM formalism and formulas to obtain a Bell State Result prediction the two questions are ;
1) is a single laser photon source with beam splitter required or can two lasers be used?
And
2) Must the two beams delivered to Alice or Bob be physically merged so they can only be measured by a single measurement device or can they skip the difficulties of merging the two beams and just combine the results from two measuring devices? (Naturally the two measuring devices working to act as one must keep their measurement angles set together) We know that the system is designed for single photon processing; so that at no time could a V> & H> both be delivered to Alice or Bob at the same time.

 

[DrChinese]

I can see that at 0° measurements made by both Alice and Bob on their share of the output from a single crystal, based on Cos² 0°; gives 1 times 1 for 100% “C” correlations. I have no problem there.

But what does this formula say about “C” when both Alice and Bob are measuring at 90° ??
And exactly what photons are Alice and Bob counting as coming from this single crystal?

A=0, B=0 does give correlations (matches) C of 1, just as you point out.
A=90, B=90 also gives correlations (matches) C of 1.
A=45, B=45 gives correlations (matches) C of .5, whereas this would have a value of 1 if the beam was entangled.

 

[DrChinese]

1. You have changed the set up to one laser as a single source of photons using a polarizing beam splitter. Why the change? And would QM formalism and formulas evaluate the two experimental systems (one laser vs. two lasers) differently.

2. But will your set up allow them to use two measuring devices each so the can measure the two beams V> & H> delivered to them independently and simply combine the detection counts before correlating between Alice & Bob.

1. I thought it made it easier to see the difference between parallel and in series. It would also be easier to calibrate and setup, I believe. Not sure if 2 lasers would work, but that isn't important either way to this experiment.

2. You cannot have 2 separate measurements on each side, because then you would know which crystal was the source. If you knew that, then the beams could not be entangled. They are only entangled when the which-path information is absent.

 

[RandallB]

A=90, B=90 also gives correlations (matches) C of 1.

Here is where I don't get how to use this "C" formula.
Both A & B see no photons at all when measuring at 90° when only using a single crystal delivering only V>V>.
So exactly what photons are being counted to give you 100%?

 

[ueit]

Sorry, in the exchange I lost the sense of what you are asserting. I don't dispute that there are a variety of ways of express entanglement and/or conversation laws besides PDC photon pairs. But they produce Bell states that have 2 important properties: they display the "perfect" correlations when measured at identical settings, and they violate Bell inequalities at specificied other settings.

On the other had, the individual streams of Type I PDC crystals show neither of these qualities. yet when 2 output streams are combined, each photon pair emerging individually gains the Bell state attributes. Now, how can a mechanical explanation provide an answer in this case? I say that the QM formalism does precisely because it is *silent* on the mechanics and does not insist on "realism". On the other hand, any realistic explanation - even non-local ones - are going to have a severe problem here. I would propose that any non-local mechanical hypothesis be required to explain this Type I PDC paradox satisfactorily without resorting to the familiar "My theory always gives the same answers as QM" mantra.

Once again, the paradox is: A single particle pair emerges in a Bell state ONLY when the output of 2 PDC crystals are combined, even though that same particle pair must emerge from the source PDC crystal *without* being a Bell state. The presence of the 2nd crystal, from which the pair could not have emerged, does nonetheless figure into the emergence of the Bell state. In a deterministic theory (as BM/dBB claims to be, for example), it must have gone through one or the other and not a superposition of both. So I say that BM/dBB cannot truly claim to be a deterministic theory and still provide an adequate explanation of this paradox.

I will argue that a “mechanistic” or classical explanation is possible for the experiment you propose and also for all of the famous quantum experiments (double slit, EPR, quantum erasers, etc.).

I will point out why the belief that QM is inherently non-classical is founded on a hidden assumption that has no justification except for our intuition that it must be true. I will also explain why this assumption is so generally accepted and why it is probably false.

I also want to stress the fact that I do not claim to have this classical interpretation of QM. What I claim is only that it is possible under some scientifically acceptable assumptions. So I wouldn’t invoke gods, aliens, conspiracies, etc.

1. What the evidence says

We know that QM is a contextual theory. The result of a measurement cannot be associated with a property of a system that exists independently of the act of measurement itself. Any non-contextual theory fails to predict correctly the EPR results. In other words, if we want a realistic theory of particles moving in a 3D space ( a classical theory, if you want) we have to accept the idea that a particle is somehow aware of what is going around it (how many detectors, pdc’s, mirrors, beam splitters, slits, etc. we have, what their state is, and so on). Of course, a particle doesn’t “know” about our understanding of how all those objects behave, it only “sees” them as big groups of other particles.

2. The classical explanation of the evidence

So, here it comes the million dollar question: is there any classical concept that can explain us how a particle “knows” the configuration of other particles? Well, I think there is such a concept and it is named FIELD. The existence of a field that is associated to each particle is enough to explain all static quantum experiments. In the single/double slit experiment, for example, the particle “knows” how many slits are there because of the field produced by the particles in the wall. One slit requires a different matter configuration than two slits, different matter configurations produce different fields and different fields correspond to different particle trajectories. The same explanation works for the experiment you propose, replace only “slit” with “pdc crystal”. There is no contradiction to classical realism whatsoever.

For the experiments testing non-locality (Aspect, delayed choice) the assumption of determinism is also required. The field remains local, but, because it evolves deterministically, the future matter configuration is encoded in it. So, our particle “knows” how it is going to be measured because the local field uniquely determines it.

So, if the particles are accompanied by a long-range local field that evolves deterministically there is no reason to reject classical realism.

3. Where the deniers of realism went wrong

If you take a look at the proposed classical explanations for various quantum experiments you will see that all of them are variations of a billiard ball model. The particles are supposed to travel in straight lines and change direction (or other properties) only at direct collisions. In your experiment you assume that a photon can be affected by the second crystal only if it passes through it. Well, such an assumption fails if the particles interact through a long-ranged field. Often I see the requirement that a particle cannot be influenced by a distant object presented as a locality condition. This is again wrong. Classical electromagnetism is local but it does not comply with such a requirement. Two charged objects interact without a direct collision.

In conclusion, the realism deniers are beating a dead horse, the billiard ball model of reality. Of course, such a model cannot explain pure classical physics like gravity or electromagnetism. It shouldn’t be a surprise that it also fail to explain QM.

4. Why the deniers of realism went wrong

One may wonder why great minds as Feynman made the same mistake of identifying classical realism with billiard balls. My guess is that we don’t directly experience a world dominated by fields (Earth gravity is an exception). Gravity is too weak to notice, electromagnetism is hidden by the fact that macroscopic object are electrically neutral. There is also the fact that these two fields decrease with the square of the distance so there exists a certain independence between the evolution of macroscopic objects.

I thing that importing the observed behavior of the macroscopic objects to the quantum world is wrong. Quantum particles may interact through a field that does not decrease with the distance. It might be periodic for example. Adding the fields produced by many particles you could still regain the inverse square law and by averaging the trajectories of many particles you could get billiard ball like trajectories. But when you deal with single particles (or entangles pairs) the things might change.

 

[RandallB]

1. I thought it made it easier to see the difference between parallel and in series. It would also be easier to calibrate and setup, I believe. Not sure if 2 lasers would work, but that isn't important either way to this experiment.

2. You cannot have 2 separate measurements on each side, because then you would know which crystal was the source. If you knew that, then the beams could not be entangled. They are only entangled when the which-path information is absent.

I'm good with #2 -- the beams must be merged.
Not so sure of #1:
Are you saying that QM formalism and formulas would interpret no special relationship between the H> and V> coming from a single polarizing beam splitter (one laser), but that it would be the same relationship between any two beams from two separate polarizing beam splitters (two lasers required)?

Sorry I think the QM formulas are a little more complete than that; and would define a significant difference between the two set ups in the formal QM math.

IMO only if QM as it currently stands defines a difference between these two set ups (and I believe the experts already do have that kind of detail even if you and I don’t understand it) and correctly uses those formulas in the single laser and splitter case can a Bell State be predicted.

But QM would not predict a Bell State for the two laser case. The QM formulas no matter how unrealistic it may seem (QM is allowed to be unrealistic) would need some imaginary "v" state or component to the H> photons produced that eventually become V>V> photon pairs. That QM "v" component for H> would travel down the V> side into the H>H> production paths. Only in the single laser set up does this imaginary piece get reintroduce with the real photon where the H> & V> beam paths are required to be merged as you said already.
And this imaginary piece in the math formalism of QM would need to be affected by the second (parallel) crystal essentially with the same formulas used when they were in series.
What all those formulas are and how they mathematically describe the effect of the second crystal on the imaginary piece going though it I do not know.
But I believe Texas or Illinois could do it on paper for you using Mathematica or the like.

As to a realistic local mechanistic explanation?
It would still depend on some physical local hidden variable following the same path I just described.
Thus this would still leave us no further than EPR in 1935.

 

[RandallB]

Here is where I don't get how to use this "C" formula.
Both A & B see no photons at all when measuring at 90° when only using a single crystal delivering only V>V>.
So exactly what photons are being counted to give you 100%?

DING – and the light bulb turns on.
DrC I finally figured out my problem with your “C”.

It is not measuring H & V.
Or even the small “v” of a polar filter as I had to be thinking.
The “C” formula is measuring all the photons all the time because it is a polarizing beam splitter that does not destroy any photons like a polar filter does; And is measuring small “v” photons as well as small “h” wrt a vertical alignment mark on the beam splitter.

Thus when the beam splitter is rotated to 90° from its perspective it has “h” in alignment with “V” as defined by the single crystal and 100% of the photons are detected as “h” by the detectors behind the two outputs of the beam splitter (not photons as ‘lost’).
I’m ok with the form of “C” ; it makes sense.

It has no effect on the issue in post 34.