Assumption: Common-space implementation comparisons

The implementation specifies:

1. ideal and actual complete preparation maps $\mathcal{P},\tilde{\mathcal{P}}$ with $d_{\diamond }(\tilde{\mathcal{P}},\mathcal{P})\le e_{\mathrm{prep}}$;

2. event Hamiltonian deviations with integrals $h_e$;

3. a collected-register channel $\tilde{\mathcal{L}}:R\to R$ with $d_{\diamond }(\tilde{\mathcal{L}},{\mathrm{id}}_R)\le e_{\mathrm{collection}}$;

4. a decoder $\tilde{\mathcal{D}}:R\to C^{(K)}$ with $d_{\diamond }(\tilde{\mathcal{D}},{\mathcal{D}}^{(K)})\le e_{\mathrm{decoder}}$.

All allowances are nonnegative. Space identifications and padding are fixed before comparison. Every inaccessible dilation output is included for complete residual claims.