Manuscript Hawk05-A@1 · Hawk05-A.tex · section · 449f85bb

Exact channels, recovery, leakage, and entropy

An explicit conserving transfer schedule › Exact channels, recovery, leakage, and entropy · lines 1001–1017

Hawk05-A@1#eq:flagN, Hawk05-A@1#eq:flagC

Suppress the stage index and write $q = q_{n}$ , $J = J_{n}$ . The channels are

N_{q} (X) C_{q} (X) = (1 - q) J X J^{†} + q Tr (X) ∣ \emptyset ⟩ ⟨ \emptyset ∣_{R}, = q X + (1 - q) Tr (X) ∣ \emptyset ⟩ ⟨ \emptyset ∣_{M} .

The occupied and vacant blocks are orthogonal.

Displayed formulas in this passage

Hawk05-A@1#eq:flagN · line 1004
$N_{q} (X) C_{q} (X) = (1 - q) J X J^{†} + q Tr (X) ∣ \emptyset ⟩ ⟨ \emptyset ∣_{R}, = q X + (1 - q) Tr (X) ∣ \emptyset ⟩ ⟨ \emptyset ∣_{M} .$
Hawk05-A@1#eq:flagC · line 1004
$N_{q} (X) C_{q} (X) = (1 - q) J X J^{†} + q Tr (X) ∣ \emptyset ⟩ ⟨ \emptyset ∣_{R}, = q X + (1 - q) Tr (X) ∣ \emptyset ⟩ ⟨ \emptyset ∣_{M} .$