Manuscript Hawk02-E@1 · Hawk02-E.tex · section · 4841592b

Complete-residual certificates and decoder certificates

Complete-residual certificates and decoder certificates · lines 1144–1160

Let

∣ Φ_{d} ⟩ = d^{- 1/2} i = 1 \sum^{d} ∣ i ⟩_{Q} ∣ i ⟩_{C}, τ_{Q} = I_{Q} / d .

For a channel $Φ$ , define the normalized Choi operator

J_{n} (Φ) = (id_{Q} \otimes Φ) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣) .

Displayed formulas in this passage

unlabeled · line 1147
$∣ Φ_{d} ⟩ = d^{- 1/2} i = 1 \sum^{d} ∣ i ⟩_{Q} ∣ i ⟩_{C}, τ_{Q} = I_{Q} / d .$
unlabeled · line 1155
$J_{n} (Φ) = (id_{Q} \otimes Φ) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣) .$