Entanglement degradation under local dissipative Landau-Zener noise

TL;DR

This work analyzes how local dissipative Landau-Zener noise degrades entanglement in a bipartite qubit system, with one qubit exposed to a time-dependent bath interaction and the other remaining isolated. By deriving a time-dependent, Markovian master equation and transforming to a rotated basis where $\tilde{H}_S(t)=Ω(t)σ_z$, the authors obtain both analytical results in the slow-driving limit and numerical insights in the fast-driving regime. A key finding is that the coupling direction, controlled by $\theta$, strongly influences entanglement: zero-temperature slow driving preserves entanglement for transversal coupling ($\theta=π/2$), and in general transversal noise is less destructive than longitudinal. Additionally, non-adiabatic dynamics (larger driving speed) tends to preserve more entanglement than adiabatic evolution, offering practical guidance for protecting entanglement against dissipative Landau-Zener noise in quantum technologies.

Abstract

We study entanglement degradation when noise on one share of an entangled pair is described by the dissipative Landau-Zener model. We show that spin-coupling direction to the environment significantly affects entanglement dynamics. In particular, for zero bath temperature in the slow-driving regime with transversal coupling, entanglement remains intact and in the fast-driving regime transversal noise have less destructive affects on entanglement compared to the longitudinal noise. Furthermore, we show that non-adiabatic dynamic is more in favour of preserving entanglement compared to adiabatic evolution.

Figures (5)

• Figure 1: Schematic representation of two qubit system, where system qubit with Landau-Zener Hamiltonian interacts with environment in a thermal state and reference qubit does not experience noise.
• Figure 2: Entanglement survival time (Eq. (\ref{['eq:ENT']})) versus temperature $T$ in slow deriving regime for $\theta=0$, $\lambda=0.1$, $\Delta=10$ and $\omega_c=\frac{\Delta}{3}$.
• Figure 3: Entanglement versuse parameter $\theta$ (in degree) for $T=0$, $\Delta=10$, $t_0=-100$, $t=100$ as given in Eq. (\ref{['eq:NT0']}).
• Figure 4: Negativity versus time for the initial state $\ket{\phi}=\frac{1}{\sqrt{2}}(\ket{00}+\ket{11})$, $\lambda=0.1$, $T=0$, $\omega_c=\frac{\Delta}{3}$, $\theta=0$ and $v=1$. From top to bottom $\Delta=0.1, 100$.
• Figure 5: Negativity versus $\frac{\Delta^2}{v}$ for $\theta=0$ (blue curve) and $\theta=\frac{\pi}{2}$ (dashed red curve) at $t=40$ when initial state is a maximally entangled state, $t_0=-40$, $T=0$, $\omega_c=\frac{\Delta}{3}$, $\lambda=0.1$ and $v=1$.