19 pages, 2 ps files This is a second replacement. In this version we include an analysis of yet another version of Bell's theorem which has been brought to our attention. We also discuss in what sense our results are related to the Wigner distribution
Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite probabilities for detecting a particle with a given spin orientation. The standard argument is that because quantum mechanics assumes that particles are emitted in a superposition of states the theory cannot produce such a set of probabilities. We examine a paper by Eberhard, and several similar papers, which claim to show that a generalized Bell inequality, the CHSH inequality, can be derived solely on the basis of the locality condition, without recourse to hidden variables. We point out that these authors nonetheless assumes a set of positive-definite probabilities, which supports the claim that hidden variables or "locality" is not at issue here, positive-definite probabilities are. We demonstrate that quantum mechanics does predict a set of probabilities that violate the CHSH inequality; however these probabilities are not positive-definite. Nevertheless, they are physically meaningful in that they give the usual quantum-mechanical predictions in physical situations. We discuss in what sense our results are related to the Wigner distribution.
Some forms of classical simulations of quantum type probabilities and correlations are capable of violating Boole's conditions of possible experience, such as the Clauser-Horne-Shimony-Holt inequality, even beyond the Tsirelson bound. This can be achieved by communicating a single bit encoding the measurement context.
A principle of information conservation is shown in abstract terms to rule out probabilistic physical laws, necessitating the existence of state trajectories. It furthermore provides a geometric-thermodynamic mechanism for the appearance of probability distributions at the operational level, and thus may provide a dynamical explanation for Born's rule of quantum probabilities. This link between geometry and operational probabilities is argued to be a promising angle from which to study the potential for "hidden information" in quantum systems, and guide efforts in quantum foundations more gene…
Research Center for Quantum Physics, National Research and Innovation Agency（量子物理研究中心，国家研究与创新署）；Department of Physics, University of Maryland, Baltimore County（马里兰大学巴尔的摩分校物理系）；Quantum Science Institute, University of Maryland, Baltimore County（马里兰大学巴尔的摩分校量子科学研究所）；National Quantum Laboratory（国家量子实验室）
Bell's theorem is supposed to exclude all local hidden-variable models of quantum correlations. However, an explicit counterexample shows that a new class of local realistic models, based on generalized arithmetic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical of two-electron singlet states. Observable probabilities are consistent with the usual arithmetic employed by macroscopic observers, but counterfactual aspects of Bell's theorem are sensitive to the choice of hidden-variable arithmetic and calculus. The model is classical in the sense of Einste…
