Thermodynamics and the quantum speed limit in the non-Markovian regime

TL;DR

This paper investigates the quantum speed limit in non-Markovian open quantum systems, deriving a thermodynamic bound applicable to general time-local evolutions and illustrating it with three qubit models.

Contribution

It generalizes the quantum speed limit bounds to non-Markovian dynamics governed by arbitrary time-local generators, extending previous Markovian results.

Findings

Derived a thermodynamic lower bound for quantum state transformation time.

Applied the bound to amplitude damping, pure dephasing, and non-Markovian evolution models.

Demonstrated the bound's validity through three qubit evolution examples.

Abstract

Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide a the lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.