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Manuscript En07-B@1 · En07-B.tex · section · 45dff4a1

Complete preservation and exact outgoing recovery

Complete preservation and exact outgoing recovery · lines 367–384

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Fix an orthonormal code basis ${∣ i ⟩}_{i = 0}^{d - 1}$ , put $E_{ij} = ∣ i ⟩ ⟨ j ∣$ , and define

∣ Φ_{d} ⟩ = d^{- 1/2} i = 0 \sum^{d - 1} ∣ i ⟩_{Q} ∣ i ⟩_{C}, P_{Φ_{d}} = ∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣ .

For a channel $Φ$ , its normalized Choi operator is

J_{n} (Φ) = (id_{Q} \otimes Φ) (P_{Φ_{d}}) .

Displayed formulas in this passage

unlabeled · line 371
$∣ Φ_{d} ⟩ = d^{- 1/2} i = 0 \sum^{d - 1} ∣ i ⟩_{Q} ∣ i ⟩_{C}, P_{Φ_{d}} = ∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣ .$
unlabeled · line 379
$J_{n} (Φ) = (id_{Q} \otimes Φ) (P_{Φ_{d}}) .$

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