Playing Dice with God
Simulating Bell's Inequality as a Game
A.J. de Weerd (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Jeroen Spandaw – Mentor (TU Delft - Analysis)
M. Blaauboer – Mentor (TU Delft - QN/Blaauboer Group)
S.K.J. Aerts – Graduation committee member (TU Delft - Numerical Analysis)
JM Thijssen – Graduation committee member (TU Delft - QN/Thijssen Group)
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Abstract
Sixty years after John Bell published his paper in which he showed that local hidden variables with statistical independence are incompatible with quantum mechanics, its implications for the nature of the universe are still hotly debated among physicists and philosophers. In his paper he showed that a universe with local hidden variables and statistical independence should satisfy Bell's inequality, but this is violated by quantum mechanics. Testing Bell's inequality turned out to be difficult, owing to a number of loopholes. These were closed in experiments in 2015 which violated Bell's inequality, putting local hidden variables with statistical independence to rest. In this paper we discuss two conceptually simple versions of Bell's inequality as a game (Maudlin and GHZ) and simulate them using Python. Using local means these games are unlikely to be won, but by utilizing the non-locality of quantum mechanics the game is expected to be won. In our simulations we find that the probability of winning decays exponentially as a function of the length of the game for local strategies in Maudlin's version and we prove that the memory loophole (also known as daily updating) will not help the participants to win. In simulating GHZ as a game we find that the game length follows a geometric distribution.