1208.5189 (Lay Nam Chang et al.)

Biorthogonal Quantum Mechanics: Super-Quantum Correlations and
Expectation Values without Definite Probabilities    [PDF]

Lay Nam Chang, Zachary Lewis, Djordje Minic, Tatsu Takeuchi

We propose mutant versions of quantum mechanics constructed on vector spaces over the finite Galois fields GF(3) and GF(9). The mutation we consider here is distinct from what we proposed in previous papers on Galois field quantum mechanics. In this new mutation, the canonical expression for expectation values is retained instead of that for probabilities. In fact, probabilities are indeterminate. Furthermore, it is shown that the mutant quantum mechanics over the finite field GF(9) exhibits super-quantum correlations (i.e. the Bell-Clauser-Horne-Shimony-Holt bound is 4). We comment on the fundamental physical importance of these results in the context of quantum gravity.

View original: http://arxiv.org/abs/1208.5189