Field extension of real values of physical observables in classical theory can help attain quantum results

TL;DR

Extending the field of physical observables from real to complex or quaternionic values in classical theories can replicate quantum correlations and resolve quantum paradoxes, challenging traditional assumptions about measurement and locality.

Contribution

This paper demonstrates that allowing complex and quaternionic values for observables in classical theories can reproduce quantum bounds and solve quantum paradoxes.

Findings

Complex-valued observables match quantum Bell bounds.

Quaternionic extension addresses GHZ paradox.

New hidden-variable model for a single qubit.

Abstract

Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what will happen if physical observables are allowed to take complex values. In this paper, we show that by allowing observables in the Bell inequality to take complex values, a classical physical theory can actually get the same upper bound of the Bell expression as quantum theory. Also, by extending the real field to the quaternionic field, we can puzzle out the GHZ problem using local hidden variable model. Furthermore, we try to build a new type of hidden-variable theory of a single qubit based on the result.