One complete joint pointer model

Let $A_{\mathrm{ptr}}$ contain $B_{\mathrm{reg}}$ pointer qubits. Its joint state is independently prepared as

Internal pointer correlations are allowed.

The ideal copying interaction is

For duration $T_R$, the bounded generator

generates it exactly.

Append a fresh finite bath $D$ in its stated state, independent of $QASR$. The actual pointer interaction is

where $L_r={L_r}^{†}$, $\Vert L_r\Vert \le 1$, are declared finite matrices on $QASD$. They may couple both registers, pointers, spectators, and bath. This is one joint bounded noise model; its terms need not factor by packet.

Define

This includes only errors during that interval. It does not purport to include an unspecified unbounded leakage process.

The pointer is destructively read in its computational basis. All of $Q,A,D$ are then discarded; $S$ is returned. Let $W_s(y\mid \mathbf{j})$ be a fixed stochastic matrix from the ideal raw pair to the reported joint record. It may include correlated assignment errors, timeout, and other declared flags.

A fresh readiness variable has failure probability $r_F$. On that branch the apparatus reports $\mathrm{reset}-\mathrm{failed}$, consumes $Q$, and returns ${\mathrm{Tr}}_{Q}X$ on $S$. No trial is deleted.