Manuscript Oai280-B@1 · Oai280-B.tex · proposition · 6d92ab75

Proposition: Compositional model comparison

Access as a circuit invariant and the complete channel › Separate model-identification and transfer bounds · lines 1161–1182 · proof included or linked

Oai280-B@1#prop:modelcomparison

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Suppose the channels have common declared interfaces and

d_{⋄} (V, V) \leq e_{V}, d_{⋄} (E_{\partial}, id_{\partial}) \leq e_{E}, d_{⋄} (D_{A}, D_{A}) \leq e_{D} .

Then

d_{⋄} (Λ_{0, A}, D_{A} N_{A}) \leq min {1, e_{V} + e_{E} + e_{D}} .

For an authorized ideal region, $D_{A} N_{A} = id_{2}$ .

Proof. Insert one intermediate composite for each component replacement. The triangle inequality and contraction of the diamond norm under CPTP pre- and postcomposition bound each replacement by its displayed allowance.

Displayed formulas in this passage

unlabeled · line 1164
$d_{⋄} (V, V) \leq e_{V}, d_{⋄} (E_{\partial}, id_{\partial}) \leq e_{E}, d_{⋄} (D_{A}, D_{A}) \leq e_{D} .$
unlabeled · line 1170
$d_{⋄} (Λ_{0, A}, D_{A} N_{A}) \leq min {1, e_{V} + e_{E} + e_{D}} .$

Proposition: Compositional model comparison

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