Manuscript Hawk05-C@1 · Hawk05-C.tex · section · ba0719f1

Complete interfaces and the two return types

Complete interfaces and the two return types · lines 287–313

Use the normalizations

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

and define

T_{τ} (X) ε_{rec} (N) δ_{full} (C) = Tr (X) τ, = D : R \to C CPTP in f d_{⋄} (DN, id_{C}), = τ_{B} \in S (B) in f d_{⋄} (C, T_{τ_{B}}) .

The diamond norm includes arbitrary reference extensions Watrous (Chapter 3). Set

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

All entropies are in bits unless a natural logarithm is printed explicitly.

Displayed formulas in this passage

unlabeled · line 296
$T_{τ} (X) ε_{rec} (N) δ_{full} (C) = Tr (X) τ, = D : R \to C CPTP in f d_{⋄} (DN, id_{C}), = τ_{B} \in S (B) in f d_{⋄} (C, T_{τ_{B}}) .$
unlabeled · line 290
$d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄},$
unlabeled · line 308
$a_{d} = 1 - d^{- 2}, b_{d} = 1 - d^{- 1} .$