馬克斯威的惡魔和量子引擎

Abstract

在這篇文章，我們研究了和馬克斯威惡魔相關的量子資訊議題。首先我們回顧了基本的Maxwell demon和Landauer`s principle，接著聚焦在熱力學和資訊理論的關係。兩者的關聯可以從熱力學第二定律裡，進而顯現出量子通訊的Holevo bound。我們從回顧一個古典粒子系統得出這個起源，並且用一個簡單的量子迴路代替，從中檢驗Holevo bound，這個檢驗是以量子邏輯閘來替代Maxwell demon。

In this thesis, we study the physics of Maxwell demon and the related issues in the context of quantum information sciences. We first review the basics of the Maxwell demon and Landauer’s principle, and then focus on the connection between thermodynamics and the information theory. This connection is manifested in a derivation of Holevo bound of quantum communication from the second law of thermodynamics. We review a classical gas model as a physical setup for this derivation. We then adopt the recent development in quantum thermodynamics and construct a simple quantum circuit model to check the Holevo bound in the context of quantum circuit model, in which the Maxwell demon is replaced by the quantum gates with or without physical memory.