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

Proposition: Logical Pauli noise

Approximate-recovery examples on the declared models › Logical Pauli and coherent errors · lines 1688–1707 · proof included or linked

Oai280-C@1#prop:pauli

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For

Γ (ρ) = p_{I} ρ + p_{X} X ρX + p_{Y} Y ρ Y + p_{Z} Z ρZ, P \sum p_{P} = 1,

d_{⋄} (Γ, id_{2}) = 1 - p_{I} .

For spectator-blind insertion before $W$ , the left subsystem decoder has the same error.

Proof. The triangle inequality gives the upper bound $1 - p_{I}$ . The Choi state is a Bell-diagonal mixture with Bell overlap $p_{I}$ , so the Bell-projector measurement gives the matching lower bound. The subsystem statement is Proposition prop:spectatorblind.

Displayed formulas in this passage

unlabeled · line 1691
$Γ (ρ) = p_{I} ρ + p_{X} X ρX + p_{Y} Y ρ Y + p_{Z} Z ρZ, P \sum p_{P} = 1,$
unlabeled · line 1695
$d_{⋄} (Γ, id_{2}) = 1 - p_{I} .$

Nearby in this section

section: Logical Pauli and coherent errors
proposition: Proposition: A coherent logical rotation
section: Logical Pauli and coherent errors