Manuscript Em04-A@2 · Em04-A-v2.tex · proposition · f5b28abc

Proposition: Deterministic detuning stability

Transient entanglement and controlled comparisons · lines 851–870 · proof included or linked

Em04-A@2#prop:disorder

For two models with the same $J, γ_{r}, γ_{d}, S_{0}$ , and Hamiltonians $h, h^{'}$ ,

d_{tr} (ρ (τ), ρ^{'} (τ)) \leq q (τ) min {1, τ c \in R in f h - h^{'} - c I_{\infty}} .

Proof. Duhamel's formula has Hermitian source $- i [h - h^{'}, S^{'} (s)]$ , of trace norm at most $2 h - h^{'} - c I_{\infty}$ . Contractivity from Lemma lem:physical proves the conditional distance bound. The vacuum weights agree, so reconstruction multiplies the conditional distance by $q$ .

Displayed formulas in this passage

unlabeled · line 855
$d_{tr} (ρ (τ), ρ^{'} (τ)) \leq q (τ) min {1, τ c \in R in f h - h^{'} - c I_{\infty}} .$

Nearby in this section

theorem: Theorem: Generation and dissipative decay
theorem: Theorem: Conditional mixing with dephasing
remark: Remark: The localized hypothesis matters
theorem: Theorem: Finite-window unitary limit
remark: Remark: Limits of these comparisons
proposition: Proposition: Two-site closed-form benchmark
section: Transient entanglement and controlled comparisons