# Terminality implies non-signalling

arXiv: https://arxiv.org/abs/1405.3681 · HTML: https://mlsanity.com/paper/1405.3681/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2014.

## Built on by (most cited first, 1 of 1)

- [Towards Compositional Interpretability for XAI](https://mlsanity.com/paper/2406.17583/) (2024)

## Abstract (arXiv)

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.