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errorcorrectionzoo · Dec 18, 2024 · e988358 · e988358
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diff --git a/codes/quantum/properties/approximate_qecc.yml b/codes/quantum/properties/approximate_qecc.yml
@@ -150,7 +150,7 @@ features:
     - 'The \textit{Petz recovery map} a.k.a. the \textit{transpose map} \cite{doi:10.1007/BF01212345,doi:10.1093/qmath/39.1.97,arxiv:1810.03150}, a quantum channel determined by the codespace and noise channel, yields an infidelity of recovery that is at most twice away from the infidelity of the best possible recovery \cite{arxiv:quant-ph/0004088}. 
     The fidelity can be expressed exactly as a function of the \term{Knill-Laflamme conditions} \cite[Thm. 1]{arxiv:2401.02022}, and it can be used to derive a generalization of the \term{Knill-Laflamme conditions} for approximate QECCs \cite{arxiv:0909.0931}.
     Satisfaction of the \term{Knill-Laflamme conditions} is sufficient but not necessary for the Petz recovery map to be the optimal recovery, and a necessary and sufficient condition has been derived \cite{arxiv:2410.23622}.
-    The infidelity of a modified Petz recovery map under erasure can be bounded using the conditional mutual information \cite{arxiv:1410.0664,arxiv:1509.07127,arxiv:1610.06169}.
+    The infidelity of a modified Petz recovery map under erasure can be bounded using the conditional mutual information via the \textit{approximate Petz theorem} \cite{arxiv:1410.0664,arxiv:1509.07127,arxiv:1610.06169}.
     In the case of topological codes, the Petz infidelity is related to the topological entanglement entropy \cite{arxiv:2408.00857}.
     Modifications include the Petz-like decoder \cite{arxiv:2405.06051}.'
     - 'The Yoshida-Kitaev decoder for the Hayden-Preskill protocol \cite{arxiv:1710.03363} can be extended to general QECCs \cite{arxiv:2405.06051}.'

diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml
@@ -121,7 +121,7 @@ features:
     - 'A color-code decoder can be used for the surface code \cite{arxiv:2306.16476}.'
     - 'Progressive-Proximity Bit-Flipping (PPBF) decoder \cite{arxiv:2402.15924}.'
     - 'Collision clustering decoder \cite{arxiv:2309.05558}.'
-    - 'Quasi-local decoder \cite{arxiv:2404.07251}.'
+    - 'Quasi-local Lindbladian decoder based on the approximate Petz theorem \cite{arxiv:2404.07251}.'
     - 'Exclusive decoder family incorporating post-selection on decoding instances deemed not too difficult \cite{arxiv:2405.03766}.'
 
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