Entangled Lotto: Simulating Mermin's Bell Gedanken Experiment

[rlduncan]

I have been developing an entangled lotto game to simulate a simple Bell gedanken experiment described by David Mermin in his article: "Is the moon there when nobody looks? Reality and the quantum theory" where the polarizations are measured at 120 degree angles. I know this is not possible for all quantum predictions, and the simulation only works for the 120 degree setting, but have I succeeded for this special case?

It is interesting that when only two orientations are considered at a time the expected outcome is observed, that is, P = (1/3)(1/2) + (2/3)(1/2) = .5. However, when the simulation takes into account the third unmeasured orientation then the quantum theory result is obtained which is P = (1/3)(1) + (2/3)(1/4) = .5.

The words "Different" and "Same" are hidden and the scratch-off method is used to reveal the random selection which is the 1/3 and 2/3 probabilities for same-switch and different-switch outcomes respectively.

Also, for the a+, b+, c+, a-, b-, c- pair selections are hidden and the scratch-off method is used to reveal the random selections for Bob and Alice.

Entangled Lotto Scratch Game Rules

1. First section is a random ordering of the words “Different”, "Different", and “Same”. Player Wins if selection reveals the word “Same”. Game Over! If Player selects “Different” they are given a second chance to Win!

2.) For Bob and Alice all a, b, c entries are always in the same relative positions and all + and - characters are anti-correlated. Player randomly selects one of six from Bob's section and randomly selects one from the three different columns of Alice's section. (Example shown below is one of 24 possible permutations that could be used to randomly generate the data set).

Lotto Ticket

Pick “Same”. You Win! Game Over!
*Different* **Same** *Different*

Pick “Different” Try Again!

Bob: Pick One
b+ a+ c-
b- a- c+

Alice: Pick One from each Column
b- a- c+
b+ a+ c-

(Ex. To Win if Bob's pick is a-, then Alice’s picks must be b- and c-)

Note: The Alice pick that’s a match to Bob’s column (switch) is a free pick and has no effect on the outcome of the other picks and there is ¼ chance that Alice’s other two picks match Bob’s.

 

[Almsco]

It sounds like you have succeeded in creating a simulation that is consistent with the expected outcomes of the Bell Gedanken experiment. It's great to see how the random ordering of words and the scratch-off method are used to reveal the random selections for Bob and Alice. Congratulations on your success!