BH12 Protocol: logical ABasis Observable adjoint

Proved

QEC.Distillation.Triorthogonal.BH12Protocol.logicalABasisObservable_adjoint

by marwahaha · Nov 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-qecert-4a64933quantum-computingquantum-error-correction

The BH12 Protocol construction uses the logical ABasis Observable adjoint property established by this source lemma. The formal statement records the complete hypotheses and conclusion.

Source: https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/Triorthogonal/Protocol.lean#L2645-L2649

Preamble

import Definitions.Def_QEC_Distillation_Triorthogonal_EvenFamily
import Definitions.Def_QEC_Distillation_Triorthogonal_NoisyInjection
import Definitions.Def_QEC_Coding_Stabilizer_JointMeasurement
import Definitions.Def_QEC_Semantics_Core_Subsystem
import Definitions.Def_QEC_Semantics_Entropy_Purification
import Definitions.Def_QEC_Distillation_Triorthogonal_Protocol
set_option autoImplicit false
noncomputable section
open QEC
open QEC.Distillation
open QEC.Distillation.Triorthogonal
open QEC.Distillation.Triorthogonal.BH12Protocol
open Semantics
open Coding
open Coding.PauliSymplectic
open BH12EvenFamily
open BH12NoisyInjection
open scoped BigOperators
attribute [local instance 100] Fintype.ofFinite
universe u

Formal statement

theorem QEC.Distillation.Triorthogonal.BH12Protocol.logicalABasisObservable_adjoint {q : Nat} (a : OddRow q) :
    LinearMap.adjoint (logicalABasisObservable a) =
      logicalABasisObservable a := by sorry

Source

https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/Triorthogonal/Protocol.lean#L2645-L2649

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