Manuscript Em05-A@1 · Em05-A-v1.tex · section · 9cac0def

Full-transfer noise: exact optimal recovery

Population-preserving dephasing with its complete environment › Full-transfer noise: exact optimal recovery · lines 945–965

Em05-A@1#eq:fullNoisy

At $η = 1$ , set

u_{λ} = a_{λ} ∣0 ⟩ + b_{λ} ∣1 ⟩, v_{λ} = a_{λ} ∣0 ⟩ - b_{λ} ∣1 ⟩ .

Their overlap is $⟨ u_{λ} ∣ v_{λ} ⟩ = λ$ .

The full-transfer noisy isometry is

V_{1, λ} ∣0 ⟩ V_{1, λ} ∣1 ⟩ = W ∣0 ⟩ \otimes ∣00 ⟩_{E} \otimes u_{λ}, = W ∣1 ⟩ \otimes ∣00 ⟩_{E} \otimes v_{λ} .

Displayed formulas in this passage

Em05-A@1#eq:fullNoisy · line 958
$V_{1, λ} ∣0 ⟩ V_{1, λ} ∣1 ⟩ = W ∣0 ⟩ \otimes ∣00 ⟩_{E} \otimes u_{λ}, = W ∣1 ⟩ \otimes ∣00 ⟩_{E} \otimes v_{λ} .$
unlabeled · line 948
$u_{λ} = a_{λ} ∣0 ⟩ + b_{λ} ∣1 ⟩, v_{λ} = a_{λ} ∣0 ⟩ - b_{λ} ∣1 ⟩ .$