Time evolution of the von Neumann entropy in open quantum system

TL;DR

This paper investigates how the von Neumann entropy evolves over time in open quantum systems governed by the Lindblad master equation, highlighting its monotonic increase under measurement-induced decoherence and providing a practical lower bound for long-term entropy.

Contribution

It introduces a general, easily calculable lower bound for the von Neumann entropy in Markovian open quantum systems, enhancing understanding of entropy dynamics.

Findings

Von Neumann entropy tends to increase monotonically under measurement decoherence.

A practical lower bound for long-time entropy is derived.

The bound applies broadly to Markovian open quantum systems.

Abstract

Control of open quantum dynamics is of great interest for realizing quantum technologies. Therefore, it is an important task to quantify and characterize the entropy for open quantum systems under decoherence. In this paper, we study the time evolution of the von Neumann entropy for open quantum systems described by the Lindblad master equation. Note that, in particular, when the decoherence corresponds to the measurement for the observable in the system, the von Neumann entropy tends to monotonically increases as the variance becomes larger. Furthermore, we present a lower bound of the von Neumann entropy in the long-time limit. This lower bound has advantages of being straightforwardly calculated and applicable to a general Markovian open quantum system.