Modal quantum theory
arXiv:1010.2929
Abstract
We present a discrete model theory similar in structure to ordinary quantum mechanics, but based on a finite field instead of complex amplitudes. The interpretation of this theory involves only the "modal" concepts of possibility and necessity rather than quantitative probability measures. Despite its simplicity, our model theory includes entangled states and has versions of both Bell's theorem and the no cloning theorem.
Presented at the 7th Workshop on Quantum Physics and Logic, Oxford University (29-30 May 2010). Revised 1 Aug 2011 in response to referee comments