Manuscript Psy02-B@2 · Psy02-B-v2.tex · section · cfd06e2e

Separate memoryless loss–dephasing model

Track A1: carrier, matched branches, and exact dynamics › Separate memoryless loss–dephasing model · lines 377–410

Psy02-B@2#eq:generator

Write

D_{L} (ρ) = L ρ L^{†} - \frac{1}{2} {L^{†} L, ρ} .

The pilot generator is

L_{R} (ρ) = - \frac{i ω}{2} [Z, ρ] + a = 0 \sum^{1} D_{κ ∣ Ω ⟩ ⟨ a ∣} (ρ) + D_{(γ + R) /2 Z} (ρ),

with $κ, γ, R \geq 0$ . The extra rate $R = E_{G} /ℏ$ is a phenomenological hypothesis.

A fresh bath qubit is prepared in $∣ 0 ⟩$ , with $⟨ 0 ∣ X_{B} ∣ 0 ⟩ = 0$ , before each collision

U_{δ t} = exp [- i γ δ t /2 Z \otimes X_{B}] .

Its code-coherence multiplier is $cos (2 γ δ t)$ . Repeated fresh collisions converge to $e^{- γ t}$ . Loss is realized by the Kraus family

K_{0} = ∣ Ω ⟩ ⟨ Ω ∣ + e^{- κ δ t /2} P, K_{a} = 1 - e^{- κ δ t} ∣ Ω ⟩ ⟨ a ∣ .

These statements specify the Markov model rather than deriving it from the thermal bath.

Displayed formulas in this passage

Psy02-B@2#eq:generator · line 384
$L_{R} (ρ) = - \frac{i ω}{2} [Z, ρ] + a = 0 \sum^{1} D_{κ ∣ Ω ⟩ ⟨ a ∣} (ρ) + D_{(γ + R) /2 Z} (ρ),$
unlabeled · line 380
$D_{L} (ρ) = L ρ L^{†} - \frac{1}{2} {L^{†} L, ρ} .$
unlabeled · line 396
$U_{δ t} = exp [- i γ δ t /2 Z \otimes X_{B}] .$
unlabeled · line 404
$K_{0} = ∣ Ω ⟩ ⟨ Ω ∣ + e^{- κ δ t /2} P, K_{a} = 1 - e^{- κ δ t} ∣ Ω ⟩ ⟨ a ∣ .$