Biorthogonal quantum mechanics: super-quantum correlations and expectation values without definite probabilities (Q2871975)

The authors study versions of quantum mechanics constructed on vector spaces over the finite Galois fields GF(3) and GF(9). Super-quantum correlations are stated in terms of the CHSH bound. As these finite fields do not possess inner products, notions such as normalizability, hermiticity and duality are reexamined by the authors in order to perform calculations such as expectation values.