Manuscript Em03-G@1 · Em03-G-v1.tex · section · 0bb3a8a3

Ordered noncommuting source dynamics

Ordered noncommuting source dynamics · lines 494–533

Em03-G@1#eq:interaction

The message is encoded by a fixed identification into the source qubit $S$ . Its computational basis is the $Z$ basis:

Z ∣ 0 ⟩ = ∣ 0 ⟩, Z ∣ 1 ⟩ = - ∣ 1 ⟩, H_{S} = 0.

The initial state is

ρ_{R S} \otimes ω_{U} .

The source and receiver have no prior message-dependent field preparation.

Choose real compact profiles $f_{1}, f_{2}$ with disjoint time slabs $I_{1} < I_{2}$ , and set $F_{j} = F [f_{j}]$ . The interaction is

H_{I} (t) = g_{1} Z \otimes Φ_{F_{1}} (t) + g_{2} X \otimes Φ_{F_{2}} (t) .

The exact measure convention is

Φ_{F} (t) = \int_{Σ_{t}} N F (t, \cdot) ϕ (t, \cdot) d Σ_{t} = \int f (t, x) Ψ (t, x) d x,

where

N = f (r), d Σ_{t} = r^{2} f (r) d x d Ω.

Thus $\int Φ_{F} (t) d t = ϕ (F)$ .

Abbreviate

a_{1} = g_{1} k (f_{1}), a_{2} = g_{2} k (f_{2}), θ = s (a_{1}, a_{2}) .

Displayed formulas in this passage

Em03-G@1#eq:interaction · line 511
$H_{I} (t) = g_{1} Z \otimes Φ_{F_{1}} (t) + g_{2} X \otimes Φ_{F_{2}} (t) .$
unlabeled · line 499
$Z ∣ 0 ⟩ = ∣ 0 ⟩, Z ∣ 1 ⟩ = - ∣ 1 ⟩, H_{S} = 0.$
unlabeled · line 503
$ρ_{R S} \otimes ω_{U} .$
unlabeled · line 517
$Φ_{F} (t) = \int_{Σ_{t}} N F (t, \cdot) ϕ (t, \cdot) d Σ_{t} = \int f (t, x) Ψ (t, x) d x,$
unlabeled · line 522
$N = f (r), d Σ_{t} = r^{2} f (r) d x d Ω.$
unlabeled · line 529
$a_{1} = g_{1} k (f_{1}), a_{2} = g_{2} k (f_{2}), θ = s (a_{1}, a_{2}) .$