Manuscript Hawk02-E@1 · Hawk02-E.tex · section · 4841592b

Packet access

Complete channels and exact microscopic accounting › Packet access · lines 719–766

Hawk02-E@1#eq:residual-ledger, Hawk02-E@1#eq:Vt, Hawk02-E@1#eq:matrix-units

Fix an orthonormal packet family $p_{1}, \dots, p_{q}$ in $h_{μ, Λ}$ , independently of any recovery optimization. Put

r = span {p_{1}, \dots, p_{q}} .

The bosonic Fock factorization is

F_{s} (h_{μ, Λ}) ≃ F_{s} (r) \otimes F_{s} (r^{⊥}) .

Define

R B = F_{s} (r), = H_{S} \otimes H_{D} \otimes F_{s} (r^{⊥}) .

The complete code isometry is

V_{t} ∣ ψ ⟩ = R (U (t) \otimes I_{D}) (W ∣ ψ ⟩ \otimes Ω_{B}),

where $R$ is the fixed regrouping into $R \otimes B$ .

The vacuum reservoir has no inaccessible preparation purifier. If a mixed reservoir preparation is substituted, its purification must be added to $B$ ; that is a different input specification.

For $Ξ_{i} (t) = V_{t} ∣ i ⟩$ ,

N_{t} (E_{ij}) = Tr_{B} ∣ Ξ_{i} (t)⟩ ⟨ Ξ_{j} (t)∣, C_{t} (E_{ij}) = Tr_{R} ∣ Ξ_{i} (t)⟩ ⟨ Ξ_{j} (t)∣ .

These formulas determine every reference-entangled input.

Displayed formulas in this passage

Hawk02-E@1#eq:residual-ledger · line 734
$R B = F_{s} (r), = H_{S} \otimes H_{D} \otimes F_{s} (r^{⊥}) .$
Hawk02-E@1#eq:Vt · line 742
$V_{t} ∣ ψ ⟩ = R (U (t) \otimes I_{D}) (W ∣ ψ ⟩ \otimes Ω_{B}),$
Hawk02-E@1#eq:matrix-units · line 757
$N_{t} (E_{ij}) = Tr_{B} ∣ Ξ_{i} (t)⟩ ⟨ Ξ_{j} (t)∣, C_{t} (E_{ij}) = Tr_{R} ∣ Ξ_{i} (t)⟩ ⟨ Ξ_{j} (t)∣ .$
unlabeled · line 724
$r = span {p_{1}, \dots, p_{q}} .$
unlabeled · line 728
$F_{s} (h_{μ, Λ}) ≃ F_{s} (r) \otimes F_{s} (r^{⊥}) .$