Toy model, contextual particles/non-contextual ensemble

[zonde]

I was trying to get answer to question if it's possible to construct non-contextual ensemble from contextual particles.
As a result I constructed this simple toy model in excel.
It is using kind of "quantum memory" as polarizer. "Quantum memory" of polarizer evolves coherently with horizontal (vertical) photons but it can evolve symmetrically or antisymmetrically in respect to combined horizontal/vertical photons from different subsequent pairs depending on absorption/re-emission of incoming photon.
Horizontal and vertical photons in addition have 0 or Pi phase i.e. symmetry or antisymmetry between different H(V) photons.
Absorption/re-emission of photon is non-contextual if polarizer is oriented at right angles but contextual (it depends from "quantum memory") for other angles. However for 45deg. angles and marginally for other angles ensemble as a whole is non-contextual.

I thought that this toy model might give some common ground for discussions of contextuality or non-contextuality of particles and ensembles.

Any comments about model or contextuality in general? Is it right to say that particles in this example are contextual but ensemble has quite non-contextual properties?

 

[DrChinese]

Any comments about model or contextuality in general? Is it right to say that particles in this example are contextual but ensemble has quite non-contextual properties?

Zonde, I have downloaded and will look at this in a bit more detail. A couple of questions:

a) I get the idea that there may be memory involved which leads to a bias. As I am sure you are aware, the De Raedt have some models around this idea too.

However, what I completely miss is the experimental side of things. This is testable! There MUST be sufficient bias that this skews the results. Therefore, you could probe it. Yet no one even bothers to do this, leading me to believe that the answer to this question is already known. (You can imagine what I think the anwer is.)


b) Can you run through an example? I see the formulae, but an example of how the bias works would be helpful. To me anyway.

 

[zonde]

a) I get the idea that there may be memory involved which leads to a bias. As I am sure you are aware, the De Raedt have some models around this idea too.

I have seen this one: http://arxiv.org/abs/1005.0906"
Idea of quantum memory sounds around the same as in my example. Only there it is applied to detector where I tried to apply it to polarizer.

However, what I completely miss is the experimental side of things. This is testable! There MUST be sufficient bias that this skews the results. Therefore, you could probe it. Yet no one even bothers to do this, leading me to believe that the answer to this question is already known. (You can imagine what I think the anwer is.)

Well, this is not exactly about testable things.
You know that Bell in his paper assumed that LHV prediction should be that each particle should produce certain result for any angle of Stern-Gerlach apparatus. That way one can get perfect correlations for any matching angles.
I am just trying to get the same effect using probabilistic outcome for single photon when polarizer is not perfectly aligned with polarization of photon.
Another thing about this model is that it is efficient detection example and consequently there are no violations of Bell or CHSH inequalities. If you intended to look for that then it might turn out to be uninteresting for you.

b) Can you run through an example? I see the formulae, but an example of how the bias works would be helpful. To me anyway.

First I take polarization as vector not just direction (up and down insted of up/down) meaning that two horizontaly polarized photons can give destructive interference if they are antisymmetric. That way projection on measurement axis of H and V photons changes sign in respect to each other as you go from one quadrant to adjacent quadrant.
Like it is illustrated in this picture. As can be seen length of projections for blue and red vector have the same sign in respect to each other in first case but opposite in second case.

Using this approach plus "quantum memory" of polarizer gives certain result even for 45deg angles but depending from sate of "quantum memory" for Alice and Bob it still gives uncertain outcome as the same state of "quantum memory" gives one result but opposite state gives opposite result.
However if depending from absorption or re-emission of H (V) photon it leaves different (opposite) states for V (H) photon then we get situation where first quartet of H/H,V/V photons synchronize "quantum memory" for Alice and Bob at the cost of randomization of first pair of photons from this quartet.
So leading edge of ensemble like "programms" polarizers to synchronized behavior.

I hope this will help to analyze the model.