Probabilistic logic of quantum observations
Logic
2018-03-20 v2 Quantum Physics
Abstract
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are assumed to imply that the underlying observables are compatible. A sound and weakly complete axiomatization is provided relying on the decidable first-order theory of real closed ordered fields. The proposed logic is proved to be a conservative extension of classical propositional logic.
Cite
@article{arxiv.1607.08369,
title = {Probabilistic logic of quantum observations},
author = {A. Sernadas and J. Rasga and C. Sernadas and L. Alcácer and A. B. Henriques},
journal= {arXiv preprint arXiv:1607.08369},
year = {2018}
}