Investigate the effects of the existence of correlation between two consecutive use of the quantum channel on quantum speed limit time

TL;DR

This paper investigates how correlations between consecutive uses of quantum channels influence the quantum speed limit time, revealing that increased correlations generally slow down quantum evolution.

Contribution

It provides the first analysis of quantum speed limit time in the context of correlated quantum channels, considering both unital and non-unital channels.

Findings

Quantum speed limit time increases with correlation strength.

Correlated pure dephasing colored noise affects evolution speed.

Correlated squeezed generalized amplitude damping channel also shows increased QSL time.

Abstract

Memory effects play an important role in the theory of open quantum systems. There are two completely independent insights about memory for quantum channels. In quantum information theory, the memory of the quantum channel is depicted by the correlations between consecutive uses of the channel on a set of quantum systems. In the theory of open quantum systems memory effects result from correlations which are created during the quantum evolution. Here, we study the quantum speed limit time for correlated quantum channel i.e. when there exist correlation between consecutive uses of quantum channel . Quantum speed limit time is the bound on the minimal time evolution between initial and target states. It is apply for quantifying the maximum speed of quantum evolution. In this work, we will consider correlated pure dephasing colored noise as an example of unital quantum channels and correlated squeezed generalized amplitude damping channel as an example of non-unital quantum channels. We evaluate the quantum speed limit time for these two channel. We find that regardless of whether the channel is unital or not, the quantum speed limit time is increased by increasing correlation between two consecutive uses of the channel.