Knill-Laflamme: ⟨i|E_a†E_b|j⟩ = α_ab δ_ij ⇔ code corrects error set {E_a}

Knill-Laflamme 1997 necessary-and-sufficient conditions for exact error correction. An error set {E_a} acting on a quantum code C = span{|ī⟩} is correctable if and only if ⟨ī|E_a†E_b|j̄⟩ = α_ab·δ_ij for all logical basis states |ī⟩, |j̄⟩…