# Quantum speedup, non-Markovianity and formation of bound state

## TL;DR

This paper clarifies that quantum speedup is solely due to the formation of system-environment bound states, not non-Markovianity, challenging previous assumptions about their relationship.

## Contribution

It demonstrates that quantum speedup depends exclusively on bound state formation, separating it from non-Markovian effects in quantum dynamics.

## Key findings

- Quantum speedup is linked only to bound state formation.
- Non-Markovianity is neither necessary nor sufficient for speedup.
- Bound states play a decisive role in accelerating quantum evolution.

## Abstract

In this paper, we investigate the relationship between the quantum speedup, nonMarkovianity and formation of a system-environment bound state. Previous results show a monotonic relation between these three such that providing stronger bound states can lead to a higher degree of non-Markovianity, and hence to greater speed of quantum evolution. By studying dynamics of a dissipative two-level system or a V-type three-level system in the presence of similar and additional systems, we reveal that the quantum speedup is exclusively related to the formation of the system-environment bound state, while the non-Markovian effect of the system dynamics is neither necessary nor sufficient to speed up the quantum evolution. In the other hand, it is demonstrated that only the formation of the system-environment bound state plays a decisive role in the acceleration of the quantum evolution.