Speed limit for open quantum systems

TL;DR

This paper derives a quantum speed limit for open systems, linking operation time with energy fluctuation and entropy production, and introduces a new quantity to characterize the speed of state transformations.

Contribution

It presents a novel inequality for open quantum systems, identifying a new speed-characterizing quantity and connecting it with control protocols like shortcuts to adiabaticity.

Findings

Derived a quantum speed limit inequality for open systems.

Identified a new quantity related to the speed of state transformation.

Connected the quantity to energy fluctuations in control protocols.

Abstract

We study the quantum speed limit for open quantum systems described by the Lindblad master equation. The obtained inequality shows a trade-off relation between the operation time and the physical quantities such as the energy fluctuation and the entropy production. We further identify a quantity characterizing the speed of the state transformation, which appears only when we consider the open system dynamics in the quantum regime. When the thermal relaxation is dominant compared to the unitary dynamics of the system, we show that this quantity is approximated by the energy fluctuation of the counter-diabatic Hamiltonian which is used as a control field in the shortcuts to adiabaticity protocol. We discuss the physical meaning of the obtained quantum speed limit and try to give better intuition about the speed in open quantum systems.