Terminality implies non-signalling

Understand

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.