Definition: Unconditional signalling test

Fix distinct event labels $p,q$, a declared class of contexts $\Gamma$, and admissible deterministic interventions $\mathcal{I},\mathcal{J}$ at $p$. All operations other than this replacement are the same within a compared pair.

For classical receiver records, let $P_{q|\mathcal{I},\Gamma }$ and $P_{q|\mathcal{J},\Gamma }$ be their unconditional laws and define

For complete channels on common input and output comparison spaces, use instead

Write $p{R}_{\inf }q$ when ${\Delta }_D(p,q)>0$. The receiver interface must not acquire the sender's record through an undeclared readout or side channel.