A theory of vectorial probability for quantum correlations

TL;DR

This paper introduces vectorial probability, a higher-dimensional geometric extension of traditional probability, to explain quantum correlations and Bell's theorem violations, suggesting a new framework for understanding quantum randomness.

Contribution

It develops a novel vectorial probability theory and constructs a local model reproducing quantum predictions, revealing the geometric origin of Bell's theorem violations.

Findings

Particle detection events exhibit four-dimensional stochasticity.

Vectorial probability geometry explains Bell's theorem violations.

Quantum systems can produce high-dimensional stochastic events.

Abstract

Randomness is a ubiquitous phenomenon that is practically accompanied by physical events described by probability theory. However, probability by definition in the theory is a nonnegative scalar quantity. Here, we propose the concept of vectorial probability, quantified as a vector with interesting but hidden geometry, and develop a theory to describe random events with correlations dictated by this geometry. Based on this theory, we construct a local model that is able to reproduce the predictions of quantum mechanics about Bell's theorem. We discover that the particle detection events in Bell experiments exhibit the stochastic nature of four-dimensional probability and that it is the unexplored geometry of the vectorial probability that is responsible for the violation of Bell's theorem. This work paves the way for generalizing probability theory from the one-dimensional probability space to higher-dimensional ones and reveals that quantum systems with correlations violating Bell's theorem are physical platforms for producing real stochastic events of high-dimensional probability.