Manuscript Hawk07-A@1 · Hawk07-A.tex · section · f9c0f5da

Norms, leakage, and quantum return

The finite model and the certificate › Norms, leakage, and quantum return · lines 367–397

For states and channels use

d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄} .

The diamond norm includes external references WatrousBook. Write

T_{τ} (X) = Tr (X) τ,

ε_{rec} (N) = D CPTP in f d_{⋄} (DN, id_{L}), δ_{full} (C) = τ \in S (B) in f d_{⋄} (C, T_{τ}) .

Set

a_{d} = 1 - d^{- 2}, b_{d} = 1 - d^{- 1} .

Entropies are in bits.

Displayed formulas in this passage

unlabeled · line 370
$d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄} .$
unlabeled · line 378
$T_{τ} (X) = Tr (X) τ,$
unlabeled · line 381
$ε_{rec} (N) = D CPTP in f d_{⋄} (DN, id_{L}), δ_{full} (C) = τ \in S (B) in f d_{⋄} (C, T_{τ}) .$
unlabeled · line 393
$a_{d} = 1 - d^{- 2}, b_{d} = 1 - d^{- 1} .$