Why the De Raedt Local Realistic Computer Simulations are wrong

[DrChinese]

In another thread, we were discussing Zonde's and the De Raedt's model for simulating Bell tests using a purported local realistic computer simulation. I have broken out into this new thread some results which will be interesting to those of you interested in this subject. I will start out by including a few relevant posts I made in that thread, and then you can skip to post #4 below to see my critique of the De Raedt models.

To give some quick background, the De Raedt simulation is intended to take the format of a typical Bell test using Alice and Bob and polarizing beam splitters. They then use a formula that acts independently on Alice and Bob to reproduce the quantum mechanical results. The idea is that independence of the formulas proves that there could be physical independence as well. If so, a local hidden variable program is possible - at least that is the claim.

 

[DrChinese]

Their (Fortran) code is at the end of http://rugth30.phys.rug.nl/pdf/COMPHY3339.pdf"

Can you help me decipher this statement:

k2=ceiling(abs(1-c2*c2)**(d/2)*r0/tau) ! delay time

this looks to me like:

k2=ceiling(abs(1-(c2*c2))**((d/2)*(r0/tau))) ! delay time

and since d=2 and static reduces to:

k2=ceiling( abs(1-(c2*c2))**(r0/tau) ) ! delay time

------------------------------------------------------------------------

After examining this statement, I believe I can find an explanation of how the computer algorithm manages to produce its results. It helps to know exactly how the bias must work. The De Raedt et al model uses the time window as a method of varying which events are detected (because that is how their fair sampling algorithm works). That means, the time delay function must be - on the average - such that events at some angle settings are more likely to be included, and events at other angle setting are on average less likely to be included. It actually does not matter what physical model they propose, because eventually they must all accomplish the same thing. And that is: the bias function must account for the difference between the graphs of the QM and LR correlation functions.

Which is simply that we want the difference between the LR correlation function and the QM correlation function to be zero at 0, 45, 90, 135 degrees. That is because there is no difference in the graphs at those angles. But there is a difference at other angles. That same difference must be positive and maximum at angles like 22.5, 157.5 etc, and be negative and minimum at angles like 67.5 and 112.5 etc. (Or maybe vice versa )

So we need an embedded bias function that has those parameters, and if their computer program is to work, we will be able to find it. Once we find it, we can then assess whether it truly models the actual experimental data. If we see it does, they win. Otherwise, they lose. Of course, my job is to challenge their model. First, I must find out how they do it.

So we know that their function must: i) alternate between positive and negative bias, ii) it must have zero crossings every 45 degrees (pi/4), and iii) it must have a period of 90 degrees (pi/2). It does not need to be perfect, because the underlying data isn't going to be perfect anyway. Any of this starting to look familiar? Why yes, that is just the kind of thing we saw in zonde's model.

 

[DrChinese]

So now, per my prior post on the De Raedt model:

Let's assume I can demonstrate how the bias function uses the delay to do its work (by affecting which events are within the time window and therefore counted). The next question is: does it model all of the data of relevant Bell tests? Well, yes and no. Obviously they claim to produce QM-like data as far as was reported - YES in this regard. But most likely we will see that the traditional Bell test experimenters did not consider this clever twist - some perhaps NO in some way. It should be possible to extend the actual experiments to show whether the De Raedt model is accurate or not. In fact, I believe I can show this without performing an experiment once I run their algorithm myself.

I think I can safely give the De Raedts an A for coming up with a simulation that works as it does. As I have said previously, a simulation which produces a QM-like result is NOT the same as a local realistic theory. So such a simulation - ALONE and BY ITSELF - is NOT a disproof of the Bell Theorem. Because there are additional consequences of any local realistic theory, and if those are not considered then it cannot be a candidate. Again, this is why Santos has failed with stochastic models.

 

[DrChinese]

HERE IS WHY THE DE RAEDT MODEL IS WRONG:

I looked at the computer simulation in some detail, and you can follow the link above to the code itself. It does in fact simulate the QM predictions, exploiting the time window/detection/unfair sampling methodology. It is common in actual Bell tests to match pairs of events using a relatively small time window. The choice of the window size determines which pairs of events are considered. They use a formula to simulate which pairs are considered, and that has the effect of creating an unfair (biased) sample. That sample then matches QM expectations, even though the full universe would not. If that actually occurred in the physical experiment itself, then it would hypothetically explain the QM results with a Local Realistic model.

Now, I have a lot of criticisms of their model. I will detail those as needed in our discussion as relevant. But what I am reporting now is that the model flat out is wrong. Here is why:

1. In the model, they do succeed in getting the Type II PDC simulation to yield results compatible with QM. They get an A for that.

2. However, those results require a polarization entangled input source. It is also possible to use their formula on a source which is NOT polarization entangled. A source which is NOT polarization entangled will not yield the QM expectation values, it will yield the Local Realistic expectation values. However, their simulation yields instead the same results as an entangled source.

3. There are several ways to get such a source as I describe. You can take a Type II PDC source and put an H filter over the Alice stream, and a V filter over the Bob stream. Or you can simply use a single Type I PDC crystal, instead of the usual 2. Either way, you have a source of paired photons which are not polarization entangled.

Therefore, their results yield the SAME expectation values regardless of whether or not the source is polarization entangled. When the actual experiement is performed in these two cases, the results are actually different. Therefore, the De Raedt model does not accurately model what is seen, while QM does.

Your comments are welcome.

 

[ajw1]

HERE IS WHY THE DE RAEDT MODEL IS WRONG:
...
2. However, those results require a polarization entangled input source. It is also possible to use their formula on a source which is NOT polarization entangled. A source which is NOT polarization entangled will not yield the QM expectation values, it will yield the Local Realistic expectation values. However, their simulation yields instead the same results as an entangled source.
...

I'm not sure what you mean. When I disable the entanglement relation (and thereby making the polarization for both photons random, I get this attached graph.

                //polarization relation
                //Particle2.Polarization = Particle1.Polarization + h.PiOver2; // polarization of particle 2

(for those who haven't read the other thread, I have changed the code from de Readt to more object orientated code, without changing the logic)

 

[DrChinese]

I'm not sure what you mean. When I disable the entanglement relation (and thereby making the polarization for both photons random, I get this attached graph.

                //polarization relation
                //Particle2.Polarization = Particle1.Polarization + h.PiOver2; // polarization of particle 2

Ah, sorry, that does NOT solve the problem at all. In fact, the De Raedts put that result in the following paper as well:

http://arxiv.org/abs/0712.2565

But that is not the problem I am referring to. In my point, the relation:

Particle2.Polarization = Particle1.Polarization + h.PiOver2; // polarization of particle 2

...holds. In other words, you cannot comment out that line! See my next post which will explain the PDC types in a little more detail. When you see this, you will realize that there are 2 separate ways to have the relation above: one which IS polarization entangled, one which is NOT polarization entangled. Only the polarization entangled version should reproduce the quantum mechanical results. The other should yield the classical curve that results from a product (separable) state.

 

[DrChinese]

For those not familar with the PDC crystal types:

Parametric down conversion (PDC) is accomplished by particular crystals with non-linear optical properties. The process is not completely understood. You see PDC crystal used in most photon entanglement experiments because all you need is a laser and a PDC crystal or 2, the crystal is cut to handle a specific input wavelength.

There are 2 types:

Type I: Produces an HH output from a V input. If you take a second Type I crystal and rotate it 90 degrees, you get VV output from an H input. Neither of these are polarziation entangled. If you put these 2 together and match the phases properly, you get polarization entanglement.

Type II: Produces an HV output from a H input, or a VH output from a V input. Neither of these are polarziation entangled. If you give the input a 45 degree tilt (half V, half H), you get polarization entanglement.

With either of the above, it is possible to have a known output with a fixed relationship between the outputs. The photons come out in pairs that are NOT entangled in polarization, but are entangled in other degrees of freedom. These do NOT produce the same statistics as polarization entangled photons although they otherwise have similar characteristics.

These pairs produce identical predictions to the polarization entangled pairs in the De Raedt model. That contradicts experiment.

 

[ajw1]

For those not familar with the PDC crystal types:

Parametric down conversion (PDC) is accomplished by particular crystals with non-linear optical properties. The process is not completely understood. You see PDC crystal used in most photon entanglement experiments because all you need is a laser and a PDC crystal or 2, the crystal is cut to handle a specific input wavelength.

There are 2 types:

Type I: Produces an HH output from a V input. If you take a second Type I crystal and rotate it 90 degrees, you get VV output from an H input. Neither of these are polarziation entangled. If you put these 2 together and match the phases properly, you get polarization entanglement.

Type II: Produces an HV output from a H input, or a VH output from a V input. Neither of these are polarziation entangled. If you give the input a 45 degree tilt (half V, half H), you get polarization entanglement.

With either of the above, it is possible to have a known output with a fixed relationship between the outputs. The photons come out in pairs that are NOT entangled in polarization, but are entangled in other degrees of freedom. These do NOT produce the same statistics as polarization entangled photons although they otherwise have similar characteristics.

These pairs produce identical predictions to the polarization entangled pairs in the De Raedt model. That contradicts experiment.

I don't think this can be a valid argument against the de Raedt model other then saying that the model doesn't describe the complete reality (as a model never does). There are a lot circumstances where it will yield results that are different from experimental observation.
As they say in several publications on this model: they don't postulate an interpretation with this model.

The model could therefore easily be adjusted to include the results for the PDC experiments as you mention, for instance by assigning a boolean property 'PDC' to each of the photons on creation (again without assigning any ontology to this property) and again treat each of them local realistic in the filters.

 

[DrChinese]

I don't think this can be a valid argument against the de Raedt model other then saying that the model doesn't describe the complete reality (as a model never does). There are a lot circumstances where it will yield results that are different from experimental observation.
As they say in several publications on this model: they don't propose an interpretation with this model.

The model could therefore easily be adjusted to include the results for the PDC experiments as you mention, for instance by assigning a boolean property 'PDC' to each of the photons on creation (again without assigning any ontology to this property) and again treat each of them local realistic in the filters.

No, that won't work either because this type of setup matches their initial assumption exactly. Both the polarization entangled and the non-polarization-entangled photons emerge from the PDC with this attribute - that the polarizations are orthogonal. They are coming out of the same crystal either way!

And sorry, but theories/hypotheses that do not match experiment usually get dropped in favor of candidates that do.

 

[ajw1]

No, that won't work either because this type of setup matches their initial assumption exactly. Both the polarization entangled and the non-polarization-entangled photons emerge from the PDC with this attribute - that the polarizations are orthogonal. They are coming out of the same crystal either way!

Maybe I wasn't clear enough in what I was trying to argue. The PDC property is not related to the Parametric down conversion process itself. It just refers to the type of particle that is produced (I might have called it 'IsEntangled' but that would have been confusing in a different way)
The point is that, apart from the polarization, I think I am allowed to use as many hidden variables as convenient, and use them in the selection process, as long as I respect locality.

And it doesn't seem difficult to extend the model for the proposed change in experimental setup to have it produce all the expected results.

 

[DrChinese]

Maybe I wasn't clear enough in what I was trying to argue. The PDC property is not related to the Parametric down conversion process itself. It just refers to the type of particle that is produced (I might have called it 'IsEntangled' but that would have been confusing in a different way)
The point is that, apart from the polarization, I think I am allowed to use as many hidden variables as convenient, and use them in the selection process, as long as I respect locality.

And it doesn't seem difficult to extend the model for the proposed change in experimental setup to have it produce the expected results.

You cannot be serious.

You may as well write a program that outputs the original Weihs et al data, and label it as a "LR" simulation program. If you have a switch in the program that changes it from "compliant dataset 1" to "compliant dataset 2" you haven't accomplished anything.

The fact is, the all of the photons are entangled and all of them are perpendicular. Some of them are also polarization entangled. If I understand you correctly, you want light to be delayed going through a filter if it is polarization entangled, but not otherwise. Right. Please do not insult the intelligence of the readers on this board. As you yourself say, we are now simply adjusting the model until the results match our conclusion, disregarding the facts.

 

[zonde]

So such a simulation - ALONE and BY ITSELF - is NOT a disproof of the Bell Theorem.

Yes, but ...
This simulation alone and by itself is clear proof about limits of applicability for Bell Theorem. And that is because Bell Theorem is mathematical no-go theorem so one mathematical counter example for the case with unfair sampling is sufficient.

2. However, those results require a polarization entangled input source. It is also possible to use their formula on a source which is NOT polarization entangled. A source which is NOT polarization entangled will not yield the QM expectation values, it will yield the Local Realistic expectation values. However, their simulation yields instead the same results as an entangled source.

The model does not claim that it explains non-entangled photons with correlated polarizations. So your argument is not valid. If you place such requirement then the model should be modified (if possible) to cover this new situation.
To me it seems that the easiest way to do this is to use two separate variables for polarization and detection delay with the same offset between them in entangled state but uncorrelated offset for detection delay variable in non-entangled state.

I think that more up to the point argument is that with this model there should be white noise outside coincidence window. But there does not seem to be such (unfortunately do not know about published results of such analysis).

 

[DrChinese]

1. Yes, but ...
This simulation alone and by itself is clear proof about limits of applicability for Bell Theorem. And that is because Bell Theorem is mathematical no-go theorem so one mathematical counter example for the case with unfair sampling is sufficient.2. The model does not claim that it explains non-entangled photons with correlated polarizations. So your argument is not valid. If you place such requirement then the model should be modified (if possible) to cover this new situation.
To me it seems that the easiest way to do this is to use two separate variables for polarization and detection delay with the same offset between them in entangled state but uncorrelated offset for detection delay variable in non-entangled state.

1. The "loophole" has a loophole.

2. Actually, it should if you follow their reasoning. However, after reading more of the De Raedt's works, it looks like they later discovered this exact issue and in fact did make changes to their models. But that is not completely clear to me at this point, as they have several papers with very similar models and nearly identical arguments.

The simulation model with code (thanks ajw1!) was entitled "A computer program to simulate Einstein–Podolsky–Rosen–Bohm experiments with photons" and was accepted for publication on 10 Jan 2007. This has the flaw present which I identified above.

Another paper, entitled "Event-based computer simulation model of Aspect-type experiments strictly satisfying Einstein’s locality conditions" was accepted for publication on 6 Aug 2007. This specifically refers to two experimental setups, called Experiment I/Type I and Experiment II/Type II, which must both be correctly described by their model. Experiment I is polarization entangled pairs which violates the Bell Inequality, and Experiment II is polarized but not entangled pairs which are separable (and therefore do not violate the Inequality). In their words (from the newer ref, page 3):

"The sources used in EPRB experiments with photons emit photons with opposite but otherwise unpredictable polarization. We refer to this experimental set-up as Experiment I. Inserting polarizers between the source and the observation stations changes the pair generation procedure such that the two photons have a fixed polarization. We refer to this set-up as Experiment II. As a result of the fixed polarization of the photons the photon intensity measured in the detectors behind the polarizers in each observation station obeys Malus’ law. Our simulation model reproduces the correct quantum mechanical behavior for the single-particle and two-particle correlation function for both types of experiments."

Further, they recognize explicitly the following two points:

a) "The difference between this model and the model described in Ref.,9 is the algorithm to simulate the polarizer. In Ref.9 we used a model for the polarizers that is too simple to correctly describe experiments of type II." I will need to do additional research to determine if the revised algorithm in this newer paper solves the issue I am identifying, or if in fact they made some other completely unrelated change. So I have some more reading to do... :)

b) They explcitly recognize that a single algorithm MUST always apply to the PDC setup, stating "...the event-by-event simulation reproduces the single- and two particle results of quantum theory for both Experiment I and II, without any change to the algorithm that simulates the polarizers." In other words, you cannot hand add the "ENTANGLED" property to the algorithm as ajw1 suggested (thankfully they acknowledge this). However, I now don't think I have the current code for this simulation model. awj1? Know where I should be looking? By the way, I did download a program from their website which does the simulation. Unfortunately, it is an EXE file and there is no source.

Regardless, I should have something more on this later today.

 

[DrChinese]

Ok, I have completed my review of the paper linked above as "Event-based computer simulation model of Aspect-type experiments strictly satisfying Einstein’s locality conditions" by De Raedt et al. It does use the same algorithm as the earlier paper.

I. In the newer paper, we have the PE (polarization-entangled) pairs as Experiment I and the results violate the Bell Inequality - and this is exactly (sometimes verbatim) the same as the earlier paper (this is the desired result).

II. In the newer paper, we have the NPE (non-polarization-entangled) pairs as Experiment II and the results do not violate the Bell Inequality (this is the desired result).

What we need to consider are the following 2 special cases of Experiment II, which I will call Experiment III and Experiment IV:

III. A subset of the Experiment II in which the angle settings of the polarizers used to get NPE pairs are set at 0 and 90 degrees only (or alternately 90 degrees and 0 degrees only). In their Experiment II, they do this but also consider other settings which are not perpendicular. So we are simply accepting those Experiment II results as valid, and being a subset of a more general rule. As before, of course, the results do not violate the Bell Inequality (this is the desired result).

IV. A setup is considered that exactly matches Experiment III above, with the exception that the polarizers used to get the NPE pairs are removed. The NPE pairs are still produced, because we also tilt the source laser by 45 degrees. This has the effect of producing the same NPE pairs but without the extra polarizers to get in the way - and which do affect the simulation. The results should still be in accordance with Experiment III, but they no longer are. Instead, they now match Experiment I. Such results are in contradiction to what is actually observed, so this is NOT the desired result.

The only problem with the above is that the authors of the paper do not include the computational algorithm for Experiments II and III, so we must take their word on the results. However, they do provide the logic for Experiments I and IV, so that we can see for ourselves. It is IV that is problematic, and matches neither the predictions of QM or of actual physical experiment.

 

[PTM19]

Can you help me decipher this statement:

k2=ceiling(abs(1-c2*c2)**(d/2)*r0/tau) ! delay time

this looks to me like:

k2=ceiling(abs(1-(c2*c2))**((d/2)*(r0/tau))) ! delay time

and since d=2 and static reduces to:

k2=ceiling( abs(1-(c2*c2))**(r0/tau) ) ! delay time

I've never used fortran but from what I was able to google the operator precedence seems to be standard with exponentiation '**' preceding over multiplication '*', shouldn't then the formula be:

k2=ceiling(((abs(1-(c2*c2))**(d/2))*r0)/tau) ! delay time

with d=2 that would reduce simply to

k2=ceiling((abs(1-(c2*c2)))*r0/tau)

I haven't read all the other posts so maybe it was already mentioned.

 

[DrChinese]

I've never used fortran but from what I was able to google the operator precedence seems to be standard with exponentiation '**' preceding over multiplication '*', shouldn't then the formula be:

k2=ceiling(((abs(1-(c2*c2))**(d/2))*r0)/tau) ! delay time

with d=2 that would reduce simply to

k2=ceiling((abs(1-(c2*c2)))*r0/tau)

I haven't read all the other posts so maybe it was already mentioned.

Yes, that is how I read it as well. I am simulating in an Excel spreadsheet with VB programming embedded so that I can check a variety of scenarios myself. Then I use Excel to graph it too. That way I can share easily. I downloaded the EXE of the De Raedt simulation itself from a site, but so far cannot actually execute it as I need the MATLAB library (but not the latest version, which I have).

 

[DrChinese]

OK, finally, I have my spreadsheet documenting the issue above on the De Raedt model. Email me or send me a message with your address and I will send to you. I will post on my site in a bit, and will post a link when available. I will upload some screen shots so you can see some of the salient points.

There are 2 images. The first shows the De Raedt model working properly for what they call Experiment I. The second shows the De Raedt model working incorrectly for a variation on their Experiment II, which I refer to as Experiment IV (the variation, that is).

 

[DrChinese]

Here are links to the spreadsheet model (Excel 2003 is .XLS, 2007 is .XLSM):

http://drchinese.com/David/DeRaedtComputerSimulation.EPRBwithPhotons.A.xls

http://drchinese.com/David/DeRaedtComputerSimulation.EPRBwithPhotons.A.xlsm

Overview:
========

This spreadsheet is based around the computer simulations of De Raedt et al per references [1] and [2] below. Generally, the papers show that Local Realistic theories could reasonably make predictions which violate a Bell Inequality.

The attached worksheet pages cover several aspects of the model, and faithfully use the published information about the model to achieve the results. The original code was in FORTRAN. In this spreadsheet, I have implemented using Visual Basic functions (VBA) which are accessible from the Visual Basic button in the Developer tab.

Conclusion
========

The results show that the De Raedt model successfully models 2 important elements of Local Realism (LR), both based around Type II PDC entanglement.

These respect Bell by assuming that the sample observed is not a fair representation of the full universe. See the worksheets "De Raedt.TypeII.Entangled" and "EventDetail".

However, the model fails to handle the situation in which the photon pairs are correlated but not polarization entangled. See the worksheet "De Raedt.TypeII.NotEntangled". According to the De Raedt Experiment II results (not simulated explicitly here), a different result should be expected which is more in line with the function .25+(cos^2(Theta)/2).

References
========

"A computer program to simulate Einstein–Podolsky–Rosen–Bohm experiments with photons" by K. De Raedt, H. De Raedt, and K. Michielsen (2007), published in Computer Physics Communications, 28 March 2007.

"Event-by-event simulation of Einstein-Podolsky-Rosen-Bohm experiments" by S. Zhao, H. De Raedt and K. Michielsen (2007), published in the Foundations of Physics.

 

[ajw1]

It seems a bit strange that http://rugth30.phys.rug.nl/eprbdemo/simulation.php" produces results around the QM prediction, while your DeRaedt results are always between this prediction and the straight line.

I have found a small error in your code, but this doesn't produce significant different results:

  k2 = ((1 - (c2 * c2)) * r0 / tau) + 1 ' delay time - exponent removed since d/2 = 1, +1 at end is equivalent to FORTRAN ceiling function

should probably be

  k2 = Math.Round(((1 - (c2 * c2)) * r0 / tau) + 0.5) ' delay time - exponent removed since d/2 = 1, +1 at end is equivalent to FORTRAN ceiling function

 

[DrChinese]

1. It seems a bit strange that http://rugth30.phys.rug.nl/eprbdemo/simulation.php" produces results around the QM prediction, while your DeRaedt results are always between this prediction and the straight line.

2. I have found a small error in your code, but this doesn't produce significant different results:

  k2 = ((1 - (c2 * c2)) * r0 / tau) + 1 ' delay time - exponent removed since d/2 = 1, +1 at end is equivalent to FORTRAN ceiling function

should probably be

  k2 = Math.Round(((1 - (c2 * c2)) * r0 / tau) + 0.5) ' delay time - exponent removed since d/2 = 1, +1 at end is equivalent to FORTRAN ceiling function

1. This is an artifact of the angles the silmultation is run at. Theirs is run at maybe 20-30 anglles randomly selected in a 90 degree range, while mine are run at evey degree. I see their results as safely within the intended range.

2. Because k2 is an integer type, the rounding causes truncation... I added +1 to the result which has the exact same effect as what you have.

 

[ajw1]

2. Because k2 is an integer type, the rounding causes truncation... I added +1 to the result which has the exact same effect as what you have.

No, not exactly (let for example c2 be 1)

 

[ajw1]

A major difference is that De Raedt's value for k is 1 (see fortran code), whereas you're model uses 30 as default for this value.

 

[DrChinese]

No, not exactly (let for example c2 be 1)

First, thank you VERY much for looking at the code.

The time window function they use has a random value associated with it, so the result cannot be a whole number.

 

[DrChinese]

A major difference is that De Raedt's value for k is 1 (see fortran code), whereas you're model uses 30 as default for this value.

That threw me at first before I realized that k=1 as a default makes no sense. That is the lowest value their routine can take and still produce a sample. Also, when you graph it - which you can in my model by setting k to be 1 - the results are very strange because there is so little data. k=30 or 10 or 100 produces more data points.

 

[ajw1]

First, thank you VERY much for looking at the code.

The time window function they use has a random value associated with it, so the result cannot be a whole number.

When you define a k3 integer using my formula and check whether a k3<>k2 occurs (set a breakpoint in the if statement) you will see the different values will occur

 

[ajw1]

That threw me at first before I realized that k=1 as a default makes no sense. That is the lowest value their routine can take and still produce a sample. Also, when you graph it - which you can in my model by setting k to be 1 - the results are very strange because there is so little data. k=30 or 10 or 100 produces more data points.

I have checked your model using k=1 (In their text they say W=k.tau) with 500000 iterations and this produces very accurate results

 

[DrChinese]

I have checked your model using k=1 (In their text they say W=k.tau) with 500000 iterations and this produces very accurate results

You are right, looks good!

 

[DrChinese]

When you define a k3 integer using my formula and check whether a k3<>k2 occurs (set a breakpoint in the if statement) you will see the different values will occur

I will try it as you say, if it produces different results I will definitely change it... my goal is a faithful representation of their simulation.

 

[zonde]

Coincidence rate for particular angle is not calculated properly in this model.
In your code there is the line:

    MainModel = MatchesWithinWindow / WithinWindow

But you should compare coincidences with coincidences at maximum angle (theta=90deg for Type II PDC) taking into account coincidences at minimum angle. Like that:
max=result at 90deg
min=result at 0deg
X=result at x angle
coincidence rate at x angle=(X-min)/(max-min)
assuming that results at all angles have the same singlet counts (or are normalized against singlet counts).
In this particular case you can look at result that is produced like that:

    MainModel = MatchesWithinWindow / Iterations

because "Iterations" faithfully represent singlet counts in this model and min=0.

And that way the model produces results that are far off from expected result.

 

[DrChinese]

Coincidence rate for particular angle is not calculated properly in this model.
In your code there is the line:

    MainModel = MatchesWithinWindow / WithinWindow

But you should compare coincidences with coincidences at maximum angle (theta=90deg for Type II PDC) taking into account coincidences at minimum angle. Like that:
max=result at 90deg
min=result at 0deg
X=result at x angle
coincidence rate at x angle=(X-min)/(max-min)
assuming that results at all angles have the same singlet counts (or are normalized against singlet counts).
In this particular case you can look at result that is produced like that:

    MainModel = MatchesWithinWindow / Iterations

because "Iterations" faithfully represent singlet counts in this model and min=0.

And that way the model produces results that are far off from expected result.

I do not follow what you are saying. Can you help me to understand better?

My model returns results (one of the options anyway) as = MatchesWithinWindow / WithinWindow for the Alice & Bob detector angle settings being some Theta between 0 and 90 degrees. So the way to compute this is: for each trial iteration, determine per the formula whether it is within the coincidence time window (which uses k, k1 and k2). If the answer is Yes, then add 1 to WithinWindow. If it is also a Coincidence (Match), then add 1 to that counter. That is the sample coincidence rate (subset of full universe) and the same way the De Raedt's report their numbers. It is the same way most papers report as well, relative to Theta.

What is your max and min, and what do they represent? I don't see this in their calculation code.

 

[DrChinese]

For example, here are trial runs that show the model working as it should (as far as I can tell anyway). Each does 500,000 iterations by degree over the range 0 to 90 degrees. One is at k=10 and the other is at k=30. Lower k means closer fit to the QM prediction. However, technically that (close fit to the QM prediction) is not a requirement of the De Raedt model. They are instead trying to show that a Bell Inequality can be violated by a simulation which exploits the fair sampling loophole, while simultaneously showing that the full universe doe NOT. I believe these 2 graphs should suffice to demonstrate that (superficially at least) for this particular setup - they call this Experiment I.

 

[DrChinese]

Here is the diagram showing a fundamental problem with the De Raedt model. It should produce identical results for Figure A and Figure B. Per the spreadsheet referenced above, it produces dramatically different results.

 

[zonde]

I do not follow what you are saying. Can you help me to understand better?

To find out result you divide coincidences in +/+ and -/- channels of PBS (drawing analogy with real experiment) with coincidences from all channels (+/+; -/-; +/-; -/+).
But suppose you have setup with polarizers not PBSes. Then you can know only say +/+ coincidences. What you do in real experiment? You run the experiment with certain angle setting for 10 second then change angle setting and run it for other 10 seconds and so on.
If you are careful you check that singlet rate does not change from one 10 sec. period to other 10 sec. period.
So in real experiment you do not compare coincidences in one channel with coincidences in all channels. You compare coincidences for different angles directly without calculating proportions like in Raedt's programm.

My model returns results (one of the options anyway) as = MatchesWithinWindow / WithinWindow for the Alice & Bob detector angle settings being some Theta between 0 and 90 degrees. So the way to compute this is: for each trial iteration, determine per the formula whether it is within the coincidence time window (which uses k, k1 and k2). If the answer is Yes, then add 1 to WithinWindow.

That means if coincidence can be detected in any channel.

If it is also a Coincidence (Match), then add 1 to that counter.

If you mean "MatchesWithinWindow" then it's coincidences in specific channel/-s as opposed to coincidences in any achannel.

That is the sample coincidence rate (subset of full universe) and the same way the De Raedt's report their numbers. It is the same way most papers report as well, relative to Theta.

What is your max and min, and what do they represent? I don't see this in their calculation code.

Yes there are noting like that in their code but it should be there if you want to mimic experiments.

 

[DrChinese]

1. To find out result you divide coincidences in +/+ and -/- channels of PBS (drawing analogy with real experiment) with coincidences from all channels (+/+; -/-; +/-; -/+).

2. Yes there are noting like that in their code but it should be there if you want to mimic experiments.

1. This is the technique used in the De Raedt simulation... so that is why I used it. I.e. to count +/+ and -/- as coincidences and the +/+; -/-; +/-; -/+ cases as being seen in ideal polarizing beam splitters with allowance made for the hypothesized "time delay" effect they exploit.

2. I prefer to stick to the simulation, because that is where I am trying to make a point. And that point is: the De Raedt model does NOT work as claimed for unentangled photon pairs with known polarizations. And that is a hard requirement for any model, as they themselves point out.

 

[ajw1]

2. I prefer to stick to the simulation, because that is where I am trying to make a point. And that point is: the De Raedt model does NOT work as claimed for unentangled photon pairs with known polarizations. And that is a hard requirement for any model, as they themselves point out.

Have you noticed they probably use a different model for their combined type I and type II experiments? They use something called a DLM (deterministic learning machine). This is not present in the model you base your conclusion on.

The
difference between this model and the model described in Ref.,9 is the algorithm to simulate
the polarizer. In Ref.9 we used a model for the polarizers that is too simple to correctly
describe experiments of type II.

See"[URL Event-based computer simulation model of Aspect-type experiments
strictly satisfying Einstein’s locality conditions[/URL]