Terminality implies non-signalling

TL;DR

This paper demonstrates that in process theories, the concept of terminality is equivalent to non-signalling when causal structure is explicitly modeled, suggesting terminality as a more fundamental principle.

Contribution

It establishes the equivalence of terminality and non-signalling in process theories with explicit causal structure, generalizing previous quantum-specific results.

Findings

Terminality and non-signalling are equivalent in process theories with explicit causal structure.

Making causal structure explicit is necessary to interpret non-signalling in process theories.

Terminality offers a simpler, more fundamental principle than non-signalling.

Abstract

A 'process theory' is any theory of systems and processes which admits sequential and parallel composition. `Terminality' unifies normalisation of pure states, trace-preservation of CP-maps, and adding up to identity of positive operators in quantum theory, and generalises this to arbitrary process theories. We show that terminality and non-signalling coincide in any process theory, provided one makes causal structure explicit. In fact, making causal structure explicit is necessary to even make sense of non-signalling in process theories. We conclude that because of its much simpler mathematical form, terminality should be taken to be a more fundamental notion than non-signalling.