Generalizations of Boxworld

TL;DR

This paper explores modifications to Boxworld, a toy nonlocal correlation theory, introducing entangled measurements, multipartite systems, and continuous classical-quantum transitions, to better understand nonlocality and entanglement.

Contribution

It presents novel extensions to Boxworld allowing entangled measurements and continuous classical-quantum transitions, expanding its applicability and analysis capabilities.

Findings

Inclusion of entangled measurements in Boxworld.

Analysis of multipartite entanglement and swapping.

Continuous transition between classical and Boxworld with maximal CHSH violation.

Abstract

Boxworld is a toy theory that can generate extremal nonlocal correlations known as PR boxes. These have been well established as an important tool to examine general nonlocal correlations, even beyond the correlations that are possible in quantum theory. We modify boxworld to include new features. The first modification affects the construction of joint systems such that the new theory allows entangled measurements as well as entangled states in contrast to the standard version of boxworld. The extension to multipartite systems and the consequences for entanglement swapping are analysed. Another modification provides continuous transitions between classical probability theory and boxworld, including the algebraic expression for the maximal CHSH violation as a function of the transition parameters.