Manuscript Psy03-B@1 · Psy03-B-v1.tex · section · 8ca3caf9

Complete feedback construction

A quantum stochastic network with a scar register › Complete feedback construction · lines 1875–1900

Psy03-B@1#eq:monotone, Psy03-B@1#eq:hybridKraus

Admitted structural-memory states are classical–quantum:

ρ_{QS} = s \sum ρ_{s} \otimes ∣ s ⟩ ⟨ s ∣, ρ_{s} \geq 0, s \sum Tr ρ_{s} = 1.

In sector $s$ , specify a complete instrument after propagation with Kraus operators $K_{r, α}^{(s)}$ :

r, α \sum K_{r, α}^{(s) †} K_{r, α}^{(s)} = I_{Q} .

The record $r$ includes any failure and erasure. Fix

f (s, r) \supseteq s

and define

V_{s, r, α} = K_{r, α}^{(s)} \otimes ∣ f (s, r)⟩ ⟨ s ∣ .

Displayed formulas in this passage

unlabeled · line 1878
$ρ_{QS} = s \sum ρ_{s} \otimes ∣ s ⟩ ⟨ s ∣, ρ_{s} \geq 0, s \sum Tr ρ_{s} = 1.$
unlabeled · line 1884
$r, α \sum K_{r, α}^{(s) †} K_{r, α}^{(s)} = I_{Q} .$
Psy03-B@1#eq:monotone · line 1890
$f (s, r) \supseteq s$
Psy03-B@1#eq:hybridKraus · line 1895
$V_{s, r, α} = K_{r, α}^{(s)} \otimes ∣ f (s, r)⟩ ⟨ s ∣ .$