Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

Contract E: readout, records, and residuals

Contract E: readout, records, and residuals · lines 323–340

For a finite-dimensional Hilbert space $H$ , write $B (H)$ for its operators. A channel is a completely positive, trace-preserving linear map. Adjoint maps use the pairing

Tr (B Φ (X)) = Tr (Φ^{*} (B) X) .

We use

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

A classical register is jointly block diagonal in its designated basis, including its correlations with all other registers. A diagonal marginal alone does not establish classicality.

Displayed formulas in this passage

unlabeled · line 329
$Tr (B Φ (X)) = Tr (Φ^{*} (B) X) .$
unlabeled · line 333
$d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄} .$