# There is no general connection between the quantum speed limit and non-Markovianity

## TL;DR

This paper demonstrates that, in general, there is no direct link between non-Markovian memory effects and the quantum speed limit in open quantum systems, with connections only in specific cases.

## Contribution

The study shows that the relationship between non-Markovianity and quantum speed limit is not universal and depends on particular dynamical classes and initial states.

## Key findings

- No general connection between non-Markovianity and quantum speed limit.
- Specific dynamical evolutions and initial states can exhibit a link.
- Results clarify the role of information back-flow in quantum evolution speed.

## Abstract

The quantum speed limit sets a bound on the minimum time required for a quantum system to evolve between two states. For open quantum systems this quantity depends on the dynamical map describing the time evolution in presence of the environment, on the evolution time {\tau} , and on the initial state of the system. We consider a general single qubit open dynamics and show that there is no simple relationship between memory effects and the tightness of the quantum speed limit bound. We prove that only for specific classes of dynamical evolutions and initial states, there exists a link between non-Markovianity and the quantum speed limit. Our results shed light on the connection between information back-flow between system and environment and the speed of quantum evolution.