Manuscript Hawk02-B@2 · Hawk02-B.tex · section · 95ea744f

Complete residual leakage

Complete residual leakage · lines 622–647

Hawk02-B@2#thm:B4, Hawk02-B@2#eq:exactleak, Hawk02-B@2#eq:uniformdecoupling

For the complete ideal complement,

δ_{leak} (C_{N}) = q_{N} (1 - \frac{1}{d ^{2}}) .

An optimal comparison state is

τ_{M, N} = (1 - q_{N}) ∣ 0 ⟩ ⟨ 0 ∣ + q_{N} J_{C} (I_{C} / d) J_{C}^{†} .

For every $ρ_{C Q}$ ,

d_{tr} ((C_{N} \otimes id_{Q}) (ρ_{C Q}), τ_{M, N} \otimes ρ_{Q}) \leq q_{N} c_{d} .

Comparison with the discharged state alone has distance $q_{N}$ .

Displayed formulas in this passage

Hawk02-B@2#eq:exactleak · line 627
$δ_{leak} (C_{N}) = q_{N} (1 - \frac{1}{d ^{2}}) .$
Hawk02-B@2#eq:uniformdecoupling · line 638
$d_{tr} ((C_{N} \otimes id_{Q}) (ρ_{C Q}), τ_{M, N} \otimes ρ_{Q}) \leq q_{N} c_{d} .$
unlabeled · line 632
$τ_{M, N} = (1 - q_{N}) ∣ 0 ⟩ ⟨ 0 ∣ + q_{N} J_{C} (I_{C} / d) J_{C}^{†} .$