Manuscript Psy02-A@1 · Psy02-A.tex · section · d92ce402

A separately specified coherence witness

Environmental dynamics and the two-budget principle › A separately specified coherence witness · lines 995–1019

Psy02-A@1#eq:coherence-witness

Use the trace and channel distances

d_{tr} (ρ, σ) = \frac{1}{2} \norm ρ - σ_{1}, d_{⋄} (Λ, Γ) = \frac{1}{2} \norm Λ - Γ_{⋄} .

For channels, the latter controls all referenced input states. The relevant operational norm facts are summarized in Watrous.

Fix a dephasing channel $Δ$ , an input state $ρ$ , and an accessible channel $Λ_{s}$ . Define

D_{s} (ρ; Λ, Δ) = \frac{1}{2} \norm Λ_{s} (ρ - Δ ρ)_{1} .

The basis, decomposition, or record algebra defining $Δ$ is part of the specification.

Displayed formulas in this passage

Psy02-A@1#eq:coherence-witness · line 1011
$D_{s} (ρ; Λ, Δ) = \frac{1}{2} \norm Λ_{s} (ρ - Δ ρ)_{1} .$
unlabeled · line 998
$d_{tr} (ρ, σ) = \frac{1}{2} \norm ρ - σ_{1}, d_{⋄} (Λ, Γ) = \frac{1}{2} \norm Λ - Γ_{⋄} .$