Some Mutant Forms of Quantum Mechanics
  We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested. 
Tatsu Takeuchi, Lay Nam Chang, Zachary Lewis, Djordje Minic
quant-ph hep-th math-ph math.MP