Manuscript Oai069-A@1 · Oai069-A.tex · section · a4913aab

Complete channels on the finite direct sums

Phase 2: positive realization and access-restricted recovery › Complete channels on the finite direct sums · lines 600–614

Oai069-A@1#eq:block-channel

For algebras

A = k ⨁ B (H_{k}), B = l ⨁ B (H^{'}_{l}),

a complete channel can be written

(Φ (ρ))_{l} = k, a \sum K_{l ∣ k, a} ρ_{k} K_{l ∣ k, a}^{†}, l, a \sum K_{l ∣ k, a}^{†} K_{l ∣ k, a} = I_{H_{k}} .

Displayed formulas in this passage

unlabeled · line 603
$A = k ⨁ B (H_{k}), B = l ⨁ B (H^{'}_{l}),$
Oai069-A@1#eq:block-channel · line 607
$(Φ (ρ))_{l} = k, a \sum K_{l ∣ k, a} ρ_{k} K_{l ∣ k, a}^{†}, l, a \sum K_{l ∣ k, a}^{†} K_{l ∣ k, a} = I_{H_{k}} .$