Manuscript Em03-E@1 · Em03-E-v1.tex · section · c4b07e6a

A Pauli-channel distance identity

E4: explicit decoder and optimal referenced recovery › A Pauli-channel distance identity · lines 861–877

Let

∣ Φ ⟩ = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2} .

For a decoder $D$ , define

ϵ_{rec} (D) = d_{⋄} (D N_{2}, id), F_{e} (D) = ⟨ Φ ∣ (id_{R} \otimes D N_{2}) (∣ Φ ⟩ ⟨ Φ ∣) ∣ Φ ⟩ .

The first is a worst-case referenced criterion; the second is the specified Bell-input test.

Displayed formulas in this passage

unlabeled · line 864
$∣ Φ ⟩ = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2} .$
unlabeled · line 868
$ϵ_{rec} (D) = d_{⋄} (D N_{2}, id), F_{e} (D) = ⟨ Φ ∣ (id_{R} \otimes D N_{2}) (∣ Φ ⟩ ⟨ Φ ∣) ∣ Φ ⟩ .$