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OrthogonalSyndromeDecoding

Abstract

Finite orthogonal syndrome copies preserve the complete logical matrix. The decoder here is support-restricted; complete-positive extension and global bundle statements are not asserted by these declarations.

Theorem 1.1 (decoding syndrome block).

Lean statement: D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.decoding_syndrome_block

Proof. Machine-checked in Lean as D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.decoding_syndrome_block (✓ std3). ∎

Source. Repository-derived.

Commentary.

Finite orthogonal syndrome copies preserve the complete logical matrix. The decoder here is support-restricted; complete-positive extension and global bundle statements are not asserted by these declarations.

Theorem 1.2 (orthogonal syndrome recovery).

Lean statement: D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.orthogonal_syndrome_recovery

Proof. Machine-checked in Lean as D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.orthogonal_syndrome_recovery (✓ std3). ∎

Source. Repository-derived.

Commentary.

Finite orthogonal syndrome copies preserve the complete logical matrix. The decoder here is support-restricted; complete-positive extension and global bundle statements are not asserted by these declarations.

Theorem 1.3 (syndrome transport orthogonal).

Lean statement: D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.syndrome_transport_orthogonal

Proof. Machine-checked in Lean as D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.syndrome_transport_orthogonal (✓ std3). ∎

Source. Repository-derived.

Commentary.

Finite orthogonal syndrome copies preserve the complete logical matrix. The decoder here is support-restricted; complete-positive extension and global bundle statements are not asserted by these declarations.

References

  • Truth anchor: D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.decoding_syndrome_block
  • Truth anchor: D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.orthogonal_syndrome_recovery
  • Truth anchor: D5/S3/Quantum/Recovery/OrthogonalSyndromeDecoding.syndrome_transport_orthogonal