Galois Field Quantum Mechanics
  We construct a discrete quantum mechanics using a vector space over the 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 discrete quantum mechanics cannot be reproduced with any hidden variable theory. 
Lay Nam Chang, Zachary Lewis, Djordje Minic, Tatsu Takeuchi
quant-ph hep-th