Manuscript En05-C@1 · En05-C.tex · proposition · aa213ea6

Proposition: Finite composition error ledger

Operational no-signalling and approximate certificates › Approximate comparison · lines 1726–1741 · proof included or linked

En05-C@1#prop:telescoping

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For compatible UCP maps $T_{j}, T_{j}$ ,

∥ T_{1} \dots T_{m} - T_{1} \dots T_{m} ∥_{cb} \leq j = 1 \sum^{m} ∥ T_{j} - T_{j} ∥_{cb} .

Proof. Replace one factor at a time. Each UCP factor is a complete contraction, so every term in the telescoping sum is bounded by the corresponding local error.

Displayed formulas in this passage

unlabeled · line 1729
$∥ T_{1} \dots T_{m} - T_{1} \dots T_{m} ∥_{cb} \leq j = 1 \sum^{m} ∥ T_{j} - T_{j} ∥_{cb} .$

Nearby in this section

section: Approximate comparison
proposition: Proposition: Tensor-free approximate cone certificate
section: Approximate comparison