# I Modeling EPR - Local or Non-Local

1. Mar 8, 2017

### edguy99

One way to talk about it precisely is in your program (great program btw). When running the program, you clearly demonstrate a difference in correlation when only "local" vs. "non-Local" variables are used. In order to help understand your program, I have modified some defaults on the program, added a log so you can see the results of each pair measurement and placed a copy here.

I see from the program that in the "Non-Local" mode you generate a pair, then take a first measure of the orientation. Using the first measure, you set the orientation of the other photon to match the measurement of the first photon, then the second photon orientation is measured. You get 100% correlation because of the resetting of the second photon after measuring the first.

In the "Local" mode, you generate the pair and measure each photon independently. I see you have introduced some randomness in the measurement and sure enough, some of the pairs do not measure the same on both ends. This means you do not get 100% correlation anymore.

In my opinion to answer your question on how to make "locality" work with your program, do what many experiments of this type do. They dont count the mis-matches in the correlation totals and assume the mis-matches were not entangled in the first place. It is important to point out that you can make the "Local" mode work in your program by assuming that any of the pairs that did not match were noise and dont count them in the correlation measurement. Your "Local" mode will have 100% correlation and will match reality!

2. Mar 8, 2017

### zonde

This is not quite correct. It is parameter called "visibility" that describes the part of the photons that are considered as not entangled. But visibility describes the fraction of photons that can be considered as random i.e. you take equal amount of matches and mis-matches. Say if you have 75% matches and 25% mis-matches then visibility is 50% (75%-25%).
Say, your simple local model can model perfect correlation with 50% visibility.

There is another loophole in most experiments. When unpaired photons are discarded experiments are open to so called detection loophole or fair sampling loophole. But you would need more complicated model to exploit that loophole.

3. Mar 8, 2017

### Boing3000

Well, not exactly. The crux of that part is that the measurement process is exactly the same in both cases( local or not). The "PolarizationTest" method contains the "measuring" logic and have NO global parameters (except the PolarizationProbability which is just a static formula).
That is also why I add the somewhat unneeded feature that Bob an Alice do their measurement in random order (to underline the fact that time/ordering/causality as no impact on the process)

This is indeed what happens, but here the crux is that it is NOT what the function do. That function have only access to one local photon and only "interact/test" with its polarization "value". The fact that that value is shared or not (non-local or local) is simply impossible for that function to know (thus no exchange of information between Alice and Bob is possible).

The reason why that method change the photon polarization (hence if shared, making all other photon sharing the same value correlated) ,is not to "implement" entanglement. It is to implement the local feature that once known that very same photon if test again by the same detect at the same angle must again be true.
Entanglement is implemented entirely inside "PrepareEntangledPair".

Actually the small trick here (except that apparently, mother nature also work this way), is that entanglement is broken AFTER the test (I have change my program accordingly to underline that)

Ho no, I will never accept that. But I've tried so many variation (generally involving random generator with seed, and stuffing more and more complex local state), that I am kind of convinced that locality cannot work ... except for supper-determinism, which is implementable localy (if you have some zillions years to wait )

4. Mar 8, 2017

### zonde

Consider more sophisticated test. One beam of entangled photons is split with PBS (polarization beam splitter) in H/V basis and then two outputs are joined back using ordinary 50/50 beam splitter. Then you measure two outputs of second beam splitter in +45/-45 basis (with additional PBSes and detectors). They should still show entanglement with the other beam according to QM.
I would say that your trick with breaking entanglement after first test will make different predictions for that more complicated test.

5. Mar 8, 2017

### Boing3000

That's an interesting case (if I understand you it involves photon quadruplets). I will try to introduce such setups in my more complete pet Bell's simulator program.
Are you saying that a photon tested/interacted with, may interact again (**) later in the same experiment ?

Anyway, I have introduce this purely as comment code. It is clearly useless for simulating Bell's proof (and a departure from Occam's path)

If a tested photon (or electron for that matter) is still fully(or at some %) entangled after testing, I don't see how it would be impossible for Bob to re-measure the photon at the same angle let's say 0.0000x sec later (photon are not very practical for this).
Should it still be 100% , even if Alice does measure at another angle in that precise space-time-window (relativity taken into account) ? What are the predictions of QM in such a case, and has that experiment been performed ?

6. Mar 8, 2017

### DrChinese

I don't know of experimental realization of this. Here is a treatment of the theory of that by Eberly:

http://www.optics.rochester.edu/~stroud/cqi/rochester/UR19.pdf

7. Mar 8, 2017

### edguy99

Did you have a particular experiment in mind when you wrote the program? In my mind, it makes me think of this experiment. You prepare a photon with a random orientation, split it, and measure in 2 locations. What the Dehlinger and Mitchell experiment has that you do not have is a coincidence detector. Have you considered adding a coincidence detector?

An important aspect to your model in "Local" mode is that you do not get 100% correlation (detection is based on probability weighted by the cos^2 of the difference in angle). In the log, every once in a while Bob and Alice are reporting "unpaired" photons. This, as I understand it, does not meet the "premise" or "assumption" of a Bell type model that you must get 100% correlation.

8. Mar 8, 2017

### Boing3000

Yep, that's exactly that one .. the simplest case possible

I don't sure I understand you. The tedious bits of comparing the matches (coincidence I guess) is done afterward, in the second main loop.

Indeed, but also with the non-local mode, just less often, meaning equal to the "strongest then classic" correlation as observed in reality.

As far as I understand, the correlation depends only on the square of the cosine between the detectors angle, and only have 100% perfect correlation at multiple of 90 degree (for spin 1 particle if my memory serves me right)

BTW I am only aware of such simple formulas about entangled properties... this one is obviously totally independent of distance or time between measure. Maybe there are other more weird quantum entangled property state that involves time and space not just "angle". It would clearly break my "model" (which is still cheaper than a lab )

Here are two graphics run of my more complete program (the horizontal axis is the angle difference, every photon plotted)
1) local (fails to emulate reality)

2) non-local (test succeeded)

9. Mar 8, 2017

### Jilang

Are you using three dimensional angles here or two?

10. Mar 8, 2017

### edguy99

From page 3 of the experiment "it is necessary to use coincidence detection to separate the downconverted photons from the background of other photons reaching the detectors... The setup is described in detail in the companion article."

I did a screenshot of a log of a sample run of your program with Bob and Alice both set at 0 degrees. #1 and #8 dont match. A coincidence detector would not consider these entangled and would not include them in the statistics. I think to model the Dehlinger and Mitchell experiment properly (the way they have done it), you would need to remove #1 and #8 as they are not "coincidences". I think this would also make significant differences in your graph of the "Local" mode.

11. Mar 8, 2017

### N88

In my opinion (in case it helps to put your mind at ease), you do not need to go beyond this: "My model is obviously totally independent of distance or time between measurements."

However, there's a rider: just so long as you maintain the pairwise comparison of outcomes with NO losses. For losses are a known loophole in many simulations, whereas QM does not need losses to derive the correct results.

PS: Every effort is (of course) made to remove unmatched (non-paired) outcomes from experimental results.

Last edited: Mar 8, 2017
12. Mar 8, 2017

### Boing3000

That's why a "virtual" lab is cheaper, and don't have to separate the noise from ... randomness

That is correct, I see no way to reproduce 100% correlation with local variable (75% is the average). Does Bell's proof rely on that ?
Remember that photon true/hidden polarization is absolutely random, and only statistical average are significant (as QM and nature seem to agree)

That may be true, but we don't have "unrealistic" lab in reality.
Ins't the coincidence detector needed to detect "false entangled" pair and remove them from the stat ?

13. Mar 8, 2017

### edguy99

Probably lots of reasons, but they are definitely taking them out.

14. Mar 8, 2017

### Boing3000

I don't see where I go beyond that. Bell's don't go beyond that either.
But in general, I would be interested to know if it exist some entangled properties that does depend on space or time or both.

I am not so much interested in margin of error happening in every experiments.
BTW there are also such "errors" in computation, where the Number.EPSILON will play a significant role.

15. Mar 8, 2017

### Boing3000

Not sure I understand. The angles are the one of the polarizers perpendicular to the photon path.
Maybe I can upgrade it to match electron spin lab (who have tree orientation dimension)

16. Mar 8, 2017

### DrChinese

The definition of a entangled pair to be included in the results is when there is one click on each side within a specified time (coincidence) window, such as less than 6 ns apart.

17. Mar 8, 2017

### entropy1

They probably take 'em out when not paired, not when not matched. Otherwise it would have to be an ideal situation.

18. Mar 8, 2017

### Boing3000

Are you aware of the same experiment but where Alice and Bob do TWO consecutive identical measurements on the same photon ?
Should not they get perfect correlation on each site separately ? or does that case fall into the "which path" case, that would imply that entanglement is clearly broken at first measurement (on either site).

That's the loophole in my model...

19. Apr 12, 2017

### Boing3000

Let's continue ... I have modified the program to handle any numbers of detectors and photons.
If I understand that article correctly it seems it is actually physically possible to entangle 4 photons polarization. So let's say we send two photons one way, and two in the opposites direction. At one end, Alice and Cathy will measure polarization (using the same random angle), and Bod an Dave will do the same at the other end (with obviously another random angle).

So my question is what is QM prediction on the correlations between A-C (that I suppose would be identical that for B-D) ?
My pet simulator will have different output if events happen in the order "A C B D" or "A B C D". (which simply correcpond to length emitter-Bob being slighlty smaller that emitter-Cathy)
So I guess nature will conspire so we cannot exchange information instantaneously just by shortening a photon path (using mirror for example). I would like to know theoretical prediction and/or if that particular setup as been tested, so I can try to fix my simulator accordingly.

20. Apr 12, 2017

### zonde

Simplified (almost correct) answer is that there are no correlations between A/C or B/D or any other pair or triplet. But if you specify three measurements you can predict the forth measurement. You have to specify entangled state to get more than simplified answer.

21. Apr 12, 2017

### Boing3000

OK, so I'll assume that correlation is A-C is 0.5 then.
I am afraid I cannot specified mathematically the state other then "maximally entangled" in the sense of testing one, would give 100% certainty on any of the other. Maybe that is simply not physically possible. I suppose that one "spontaneous parametric down conversion" follow by two other on each branch won't guarantee the that the 4 photon are entangled (just pairs of them).

Anyway your answer seems to imply that if A-B-C used a specified setup, D could be predicted. So I am wondering what would avoid A-C to "change their mind". Thus allowing B-D to instantaneously know that the agreed on protocol is no more followed.

Beside I have another more statistic/math question. As an output of simulated experiments I just get a array of angle/pass per detector. To make sense of them I simply count the number of "matches" between pairs of two detector. But I cannot figure out a way to do that without having to use again a random() against the chances of being correlated (given the delta between angle detector).
It kind of bothers me that each time I "analyse" the same static result, I get a slightly different answer.

22. Apr 12, 2017

### zonde

Let's say we take GHZ state $\frac12(|HHHH\rangle+|VVVV\rangle)$. If you measure all photons in H/V basis then indeed measuring one photon as H you can predict that any other will be H as well. But if you measure in other bases (diagonal and circular) you have to express measured polarizations in H/V basis and sum all relative phases between H/V modes and sum has to be 0 to get certain outcome.
You can take a look at this post. There is a link to description of GHZ experiment and in the post is heuristic principle how to make sense of measurements without deep knowledge of math.

23. Apr 12, 2017

### Boing3000

Thank you for those answers ! I hope that by "measure in other base" you mean orientation of detector, and not some transformation in nth dimensional (here 4?) Hilbert space.