Causality and Duality in Multipartite Generalized Probabilistic Theories

TL;DR

This paper explores the fundamental connection between causality frameworks in physics, establishing a duality between no-signaling principles and classical processes, and introduces a multipartite classical process extending quantum switch concepts.

Contribution

It demonstrates a duality between causality frameworks in GPTs and process matrix frameworks, and introduces a multipartite classical process extending quantum switch capabilities.

Findings

Established duality between no-signaling and classical processes in tripartite systems

Extended results to multipartite systems, linking different causality frameworks

Proposed a 4-partite classical process extending quantum switch with certification inequality

Abstract

Causality is one of the most fundamental notions in physics. Generalized probabilistic theories (GPTs) and the process matrix framework incorporate it in different forms. However, a direct connection between these frameworks remains unexplored. By demonstrating the duality between no-signaling principle and classical processes in tripartite classical systems, and extending some results to multipartite systems, we first establish a strong link between these two frameworks, which are two sides of the same coin. This provides an axiomatic approach to describe the measurement space within both box world and local theories. Furthermore, we describe a logically consistent 4-partite classical process acting as an extension of the quantum switch. By incorporating more than two control states, it allows both parallel and serial application of operations. We also provide a device-independent certification of its quantum variant in the form of an inequality.