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

The full complementary channel and leakage constants

The full complementary channel and leakage constants · lines 948–972

Em03-E@1#eq:dephcomplement

Define the complementary dephasing channel

C_{η} (X) = x = 0 \sum^{1} ⟨ x ∣ X ∣ x ⟩ ∣ e_{x} ⟩ ⟨ e_{x} ∣ .

Let

W_{ab} = (P_{ab} \otimes I_{Z_{e}}) W_{η} .

The occupation-source complement is the independent density

δ_{A} = i = 1 ⨂^{2} n = 0 \sum^{J_{i}} w_{i, n} ∣ d_{n} ⟩ ⟨ d_{n} ∣_{A_{i}} .

Suppress the fixed terminal $F_{1} = 0$ and all fixed initial factors. The fuel $F_{2}$ labels two orthogonal complementary sectors: success $F_{2} = 0, Q = 0$ , and failure $F_{2} = 1$ .

Displayed formulas in this passage

Em03-E@1#eq:dephcomplement · line 952
$C_{η} (X) = x = 0 \sum^{1} ⟨ x ∣ X ∣ x ⟩ ∣ e_{x} ⟩ ⟨ e_{x} ∣ .$
unlabeled · line 958
$W_{ab} = (P_{ab} \otimes I_{Z_{e}}) W_{η} .$
unlabeled · line 962
$δ_{A} = i = 1 ⨂^{2} n = 0 \sum^{J_{i}} w_{i, n} ∣ d_{n} ⟩ ⟨ d_{n} ∣_{A_{i}} .$

The full complementary channel and leakage constants

Displayed formulas in this passage

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