Manuscript Em03-E@1 · Em03-E-v1.tex · theorem · c4b07e6a

Theorem: End-to-end coherent recovery

E5: constructed coherent access and decoder implementation › An executable complete decoder · lines 1547–1580 · proof included or linked

Em03-E@1#thm:endrecovery, Em03-E@1#eq:endrecovery

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For the implemented dynamics, whole-block coherent access, and complete decoder,

d_{⋄} (D A N_{2}, id) \leq min {1, \frac{3 - p - 2 p η}{4} + ϵ_{dyn} + ϵ_{acc} + ϵ_{dec}} .

The corresponding Bell-test fidelity is at least

max {0, \frac{1 + p + 2 p η}{4} - ϵ_{dyn} - ϵ_{acc} - ϵ_{dec}} .

Proof. The exact composed channel is (eq:decoded). The three complete-channel comparisons telescope through the same intermediate interfaces. Apply Theorem thm:recovery and effect contraction for the Bell test.

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Em03-E@1#eq:endrecovery · line 1551
$d_{⋄} (D A N_{2}, id) \leq min {1, \frac{3 - p - 2 p η}{4} + ϵ_{dyn} + ϵ_{acc} + ϵ_{dec}} .$
unlabeled · line 1565
$max {0, \frac{1 + p + 2 p η}{4} - ϵ_{dyn} - ϵ_{acc} - ϵ_{dec}} .$

Theorem: End-to-end coherent recovery

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