# Quantum speed limit time for correlated quantum channel

## TL;DR

This paper investigates how correlations in quantum channels affect the quantum speed limit time, revealing that increased correlation strength can either increase or decrease the limit depending on the channel type.

## Contribution

It provides a detailed analysis of quantum speed limit times for correlated unital and non-unital channels, highlighting the impact of correlation strength on evolution speed.

## Key findings

- Correlated dephasing colored noise increases quantum speed limit time with more correlation.
- Correlated amplitude damping decreases quantum speed limit time as correlation increases.
- Correlated squeezed generalized amplitude damping decreases quantum speed limit time with higher correlation.

## Abstract

Memory effects play a fundamental role in the dynamics of open quantum systems. There exist two different views on memory for quantum noises. In the first view, the quantum channel has memory when there exist correlations between successive uses of the channels on a sequence of quantum systems. These types of channels are also known as correlated quantum channels. In the second view, memory effects result from correlations which are created during the quantum evolution. In this work we will consider the first view and study the quantum speed limit time for a correlated quantum channel. Quantum speed limit time is the bound on the minimal time which is needed for a quantum system to evolve from an initial state to desired states. The quantum evolution is fast if the quantum speed limit time is short. In this work, we will study the quantum speed limit time for some correlated unital and correlated non-unital channels. As an example for unital channels we choose correlated dephasing colored noise. We also consider the correlated amplitude damping and correlated squeezed generalized amplitude damping channels as the examples for non-unital channels. It will be shown that the quantum speed limit time for correlated pure dephasing colored noise is increased by increasing correlation strength, while for correlated amplitude damping and correlated squeezed generalized amplitude damping channels quantum speed limit time is decreased by increasing correlation strength.