Assumption: Capacity-N structural class

A capacity-$N$ strategy $\mathsf{S}=(\mathsf{P},\mathsf{U})$ supplies, for every $\left|L\right|\le N$ and $S\subseteq L$:

1. a normalized law ${{\mathsf{P}}^{\mathsf{S}}}_{\psi }$ on $\{0,1{\}}^S$;

2. a pure unit residual ray ${{\mathsf{U}}^{\mathsf{S}}}_{\psi }(\kappa )\in \mathbb{P}({\mathcal{H}}_{L\setminus S})$ whenever ${{\mathsf{P}}^{\mathsf{S}}}_{\psi }(\kappa )>0$.

These data depend only on the current ray and measured names. They are equivariant under simultaneous relabeling of names, tensor factors, and outcome coordinates.

All finite-register unitaries and fresh $|0⟩$ allocation have their stipulated linear-algebraic meanings. Allocation is allowed only when the resulting live occupancy is at most $N$. No hidden memory, silent quantum deletion, or apparatus-dependent measurement parameter is included.

A finite experimental program uses allocation, gates, destructive readout, finite classical control, and return. Every quantum name is consumed or returned. Local programs exchange neither quantum names nor classical messages. Single programs use their prescribed evaluation order; bipartite experiments permit interleavings of their local orders.

For $S=\varnothing$, readout has its unique unit outcome and leaves the state unchanged.