Manuscript Oai280-C@1 · Oai280-C.tex · proposition · 7d44b8c0

Proposition: Successful-branch trap

Complete branches and approximation budgets · lines 1202–1221 · proof included or linked

Oai280-C@1#prop:branchtrap

Consider the complete qubit channel

Γ_{η} = η id_{2} + (1 - η) Dep_{2}, 0 \leq η \leq 1.

A success flag may identify the identity branch with conditional Bell fidelity one. If the returned output discards that flag, then

d_{⋄} (Γ_{η}, id_{2}) = \frac{3}{4} (1 - η) .

Proof. The complete channel difference is $(1 - η) (Dep_{2} - id_{2})$ . Theorem thm:block gives the stated norm.

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