Manuscript Em03-E@1 · Em03-E-v1.tex · section · c4b07e6a

Two radiation cells

E0: message, source, environments, and emitted cells › Two radiation cells · lines 318–354

Each emitted cell has an occupation register and a payload register:

r_{1} = O_{1} C_{1}, r_{2} = O_{2} C_{2} .

The occupation spaces are

H_{O_{i}} = span {∣ 0 ⟩, \dots, ∣ J_{i} ⟩}, H_{O_{i}} = ω_{i}^{cell} n = 0 \sum^{J_{i}} n ∣ n ⟩ ⟨ n ∣ .

The first payload space has basis

∣ v ⟩_{1}, ∣ a, b ⟩_{1}, a, b \in {0, 1},

and the second has basis

∣ v ⟩_{2}, ∣ 0 ⟩_{o}, ∣ 1 ⟩_{o} .

Their free Hamiltonians are

H_{C_{1}} = ε_{cell} a, b \sum ∣ a, b ⟩ ⟨ a, b ∣, H_{C_{2}} = ε_{cell} x = 0 \sum^{1} ∣ x_{o} ⟩ ⟨ x_{o} ∣ .

All cells begin in

∣ 0 ⟩_{O_{1}} ∣ v ⟩_{C_{1}} ∣ 0 ⟩_{O_{2}} ∣ v ⟩_{C_{2}} .

The occupied payload labels are degenerate internal states. They are additional model degrees of freedom, not unmentioned scalar-field packet modes.

Displayed formulas in this passage

unlabeled · line 321
$r_{1} = O_{1} C_{1}, r_{2} = O_{2} C_{2} .$
unlabeled · line 325
$H_{O_{i}} = span {∣ 0 ⟩, \dots, ∣ J_{i} ⟩}, H_{O_{i}} = ω_{i}^{cell} n = 0 \sum^{J_{i}} n ∣ n ⟩ ⟨ n ∣ .$
unlabeled · line 331
$∣ v ⟩_{1}, ∣ a, b ⟩_{1}, a, b \in {0, 1},$
unlabeled · line 335
$∣ v ⟩_{2}, ∣ 0 ⟩_{o}, ∣ 1 ⟩_{o} .$
unlabeled · line 339
$H_{C_{1}} = ε_{cell} a, b \sum ∣ a, b ⟩ ⟨ a, b ∣, H_{C_{2}} = ε_{cell} x = 0 \sum^{1} ∣ x_{o} ⟩ ⟨ x_{o} ∣ .$
unlabeled · line 346
$∣ 0 ⟩_{O_{1}} ∣ v ⟩_{C_{1}} ∣ 0 ⟩_{O_{2}} ∣ v ⟩_{C_{2}} .$