Manuscript Em05-B@1 · Em05-B-v1.tex · section · 6c050f5b

Full transfer: exact optimal recovery

Population-preserving dephasing and its full environment › Full transfer: exact optimal recovery · lines 1638–1661

Em05-B@1#eq:fullNoisyIsometry

At $η = 1$ , put

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

Then $⟨ u_{λ} ∣ v_{λ} ⟩ = λ$ , and

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-B@1#eq:fullNoisyIsometry · line 1653
$V_{1, λ} ∣0 ⟩ V_{1, λ} ∣1 ⟩ = W ∣0 ⟩ \otimes ∣00 ⟩_{E} \otimes u_{λ}, = W ∣1 ⟩ \otimes ∣00 ⟩_{E} \otimes v_{λ} .$
unlabeled · line 1641
$u_{λ} = a_{λ} ∣0 ⟩ + b_{λ} ∣1 ⟩, v_{λ} = a_{λ} ∣0 ⟩ - b_{λ} ∣1 ⟩ .$