Manuscript Em03-C@1 · Em03-C-v1.tex · theorem · 47dd71ec

Theorem: Complete-record comparison in every setting

C2: information-sensitive finite-register measurements › A declared rotation family · lines 1758–1783 · proof included or linked

Em03-C@1#thm:settings, Em03-C@1#eq:settingbudget

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Let $ρ_{12 S R} = I_{H} (ρ_{v_{L} S R})$ . For each number or Pauli setting $s$ , the complete model record obeys

d_{tr} (Ξ_{s, F S R}, (P_{s}^{S} \otimes id_{R}) (B_{a} \otimes id_{S R}) (ρ_{12 S R})) \leq e_{s} := min {1, η + γ_{s} + δ_{s}} .

For the number setting, $γ_{Z} = 0$ and the ideal target is (eq:jointrecord).

Proof. Telescope through ideal transfer, ideal setting rotation, and ideal pointer readout. Their errors are respectively Theorem thm:transfer, Lemma lem:stability, and Theorem thm:readout. Every intermediate interface includes $S$ and the appended reference $R$ .

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Em03-C@1#eq:settingbudget · line 1763
$d_{tr} (Ξ_{s, F S R}, (P_{s}^{S} \otimes id_{R}) (B_{a} \otimes id_{S R}) (ρ_{12 S R})) \leq e_{s} := min {1, η + γ_{s} + δ_{s}} .$

Theorem: Complete-record comparison in every setting

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