# Quantum speed limit time in the presence of disturbance

## TL;DR

This paper investigates how disturbance effects in an environment influence the quantum speed limit time, showing that non-Markovian effects caused by disturbances can accelerate quantum evolution.

## Contribution

It introduces a model analyzing the impact of environmental disturbances on quantum speed limit time, highlighting the role of non-Markovian effects in this process.

## Key findings

- Disturbance effects reduce quantum speed limit time.
- Non-Markovian effects emerge due to environment interaction.
- Different spectral densities influence the dynamics.

## Abstract

Quantum theory sets a bound on the minimal time evolution between initial and target states. This bound is called as quantum speed limit time. It is used to quantify maximal speed of quantum evolution. The quantum evolution will be faster, if quantum speed limit time decreases. In this work, we study the quantum speed limit time of a quantum state in the presence of disturbance effects in an environment. We use the model which is provided by Masashi Ban in \href{https://doi.org/10.1103/PhysRevA.99.012116}{Phys. Rev. A 99, 012116 (2019)}. In this model two quantum systems $\mathcal{A}$ and $\mathcal{S}$ interact with environment sequentially. At first, quantum system $\mathcal{A}$ interacts with the environment $\mathcal{E}$ as an auxiliary system then quantum system $\mathcal{S}$ interacts with disturbed environment immediately. In this work, we consider dephasing coupling with two types of environment with different spectral density: Ohmic and Lorentzian. We observe that, non-Markovian effects will be appear in the dynamics of quantum system $\mathcal{S}$ by the interaction of quantum system $\mathcal{A}$ with the environment. Given the fact that quantum speed limit time reduces due to non-Markovian effects, we show that disturbance effects will reduce the quantum speed limit time.