Corollary: Accuracy and causal safety are independent obligations

A causally embedded implementation has exact zero signalling outside its certified physical past, irrespective of its accuracy. If its target has signalling $s_0$ on a forbidden pair, any half-diamond approximation to that target has error at least $s_0/2$. Conversely, an arbitrarily accurate approximation to a nonsignalling target need not be exactly nonsignalling.

Proof. Use Theorems thm:physical and thm:signal-stability. For the last assertion,

on a qubit differs from the constant channel ${\mathcal{R}}_0$ by half-diamond distance at most $ϵ$, but has signalling $ϵ$ between its input and output.