Manuscript Oai272-A@1 · Oai272-A.tex · proposition · a40828a0

Proposition: Complete-interface robustness

Conditioning, implementation error, and protocol restrictions · lines 1051–1072 · proof included or linked

Oai272-A@1#prop:robust

Suppose a certified ideal output has gap $1/5 - 2 κ$ , and an implemented output on the same bit–Eve interface satisfies

d_{tr} (τ, τ) \leq b .

Then its distance from every ideal bit obeys

d_{tr} (τ, γ^{(1)}_{σ}) \geq max {0, 1/10 - κ - b} .

Compatible stepwise half-diamond allowances $b_{1}, \dots, b_{m}$ give the valid choice $b \leq min {1, \sum_{j} b_{j}}$ .

Proof. Use the triangle inequality and telescope compatible channel compositions. Pre- and postcomposition by channels contract diamond distance.

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