Exact Pauli-detecting codes form continuous connected families in a variance geometry parameterized by λ* from Knill-Laflamme conditions, with stabilizer codes occupying only discrete measure-zero subsets.
A fundamental constraint is eigenvalue interlacing: ifE has eigenvaluesλ 1 ≥λ 2 ≥λ 3 onH 0, then any scalar compressionP EP=αPmust satisfyα=λ 2
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Variance Geometry of Exact Pauli-Detecting Codes: Continuous Landscapes Beyond Stabilizers
Exact Pauli-detecting codes form continuous connected families in a variance geometry parameterized by λ* from Knill-Laflamme conditions, with stabilizer codes occupying only discrete measure-zero subsets.