Manuscript Em03-B@2 · Em03-B-v2.tex · theorem · c1a0977d

Theorem: Apparatus-model realization of the finite Hawking readout

End-to-end theorem and constructive tolerances › The model-level theorem · lines 1850–1893 · proof included or linked

Em03-B@2#thm:model, Em03-B@2#eq:modelrecord, Em03-B@2#eq:modelbounds

Retain Assumption ass:field, the weighted test completion, the finite-window construction, and the model specifications for capture, controls, independent preparations, and readout. The input has the specified participating Gaussian marginal and any admitted normal spectator–reference extension.

The complete model record obeys

d_{tr} (Ξ_{F S R}^{model}, Ω_{N, S R} (Tr_{g} ρ)) \leq e_{N, K}^{model} .

Its decoded statistics obey

∣ E_{model} κ - ν_{h} ∣ d_{TV} (p_{model}, p_{h}) \leq ν_{h} q_{h}^{N} + N e_{N, K}^{model}, \leq min {1, q_{h}^{N + 1} + e_{N, K}^{model}} .

The decoded complete-record comparison with the unsaturated number record retains spectators and references and has the same bound as the second line.

For the finite Enter terminology, also retain Assumption ass:I.

Proof. Theorem thm:transfer supplies the transfer certificate from the capture kernel, preparation, pulses, and control domain. Theorem thm:readbudget supplies the complete-instrument certificate from its specified components. Substitute both into Theorem thm:interface.

Displayed formulas in this passage

Em03-B@2#eq:modelrecord · line 1859
$d_{tr} (Ξ_{F S R}^{model}, Ω_{N, S R} (Tr_{g} ρ)) \leq e_{N, K}^{model} .$
Em03-B@2#eq:modelbounds · line 1868
$∣ E_{model} κ - ν_{h} ∣ d_{TV} (p_{model}, p_{h}) \leq ν_{h} q_{h}^{N} + N e_{N, K}^{model}, \leq min {1, q_{h}^{N + 1} + e_{N, K}^{model}} .$

Theorem: Apparatus-model realization of the finite Hawking readout

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