Manuscript Hawk06-A@1 · Hawk06-A.tex · section · c59fe67c

The complete finite model

The complete finite model · lines 357–386

and entropy conventions. We use

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

T_{τ} (X) = Tr (X) τ,

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

Diamond distance includes arbitrary external references WatrousBook. Set

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

All entropies below are in bits.

Displayed formulas in this passage

unlabeled · line 361
$d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄},$
unlabeled · line 365
$T_{τ} (X) = Tr (X) τ,$
unlabeled · line 368
$ε_{rec} (N) = D CPTP in f d_{⋄} (DN, id_{L}), δ_{full} (C) = τ in f d_{⋄} (C, T_{τ}) .$
unlabeled · line 381
$a_{d} = 1 - d^{- 2}, b_{d} = 1 - d^{- 1} .$