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.

[1] Peres A. Quantum Theory: The Concepts and Methods. Kluwer Academic publisher, 1993.
[2] Artyom Petrosyan, Sergio Ciliberto, Raoul Dillenschneider, Eric Lutz, Antoine Bérut, Artak Arakelyan. Experimental verification of landauer’s
principle linking information and thermodynamics. Nature, 483:187–189,
Mar 2012.
[3] Charles H. Bennett. Logical reversibility of computation. IBM Journal
of Research and Development, 17:525–532, Nov 1973.
[4] Charles H. Bennett. The thermodynamics of computation—a review.
International Journal of Theoretical Physics, 21:905–940, Dec 1982.
[5] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa,
Asher Peres, and William K. Wootters. Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Phys.
Rev. Lett., 70:1895–1899, Mar 1993.
[6] Isaac L Chuang, Daniel Gottesman. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 402:390–393, Oct 1999.
[7] Časlav Brukner Koji Maruyama and Vlatko Vedral. Thermodynamical
cost of accessing quantum information. Journal of Physics A: Mathematical and General, 38:71–75, Jul 2005.
[8] R. Landauer. Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5:183–191, July 1961.
[9] Alfred Lande. Thermodynamic continuity and quantum principles.
Phys. Rev., 87:267–271, Jul 1952.
51
[10] Koji Maruyama, Franco Nori, and Vlatko Vedral. Colloquium: The
physics of maxwell’s demon and information. Rev. Mod. Phys., 81:1–23,
Jan 2009.
[11] John William Strutt Baron Maxwell, James Clerk; Rayleigh. Theory of
heat. 1908.
[12] V. Vitelli M.B. Plenio. The physics of forgetting: Landauer’s erasure
principle and information theory. Contemporary Physics, 42:25–60, Mar
2001.
[13] Barbara Piechocinska. Information erasure. Phys. Rev. A, 61:062314,
May 2000.
[14] H. T. Quan, Yu-xi Liu, C. P. Sun, and Franco Nori. Quantum thermodynamic cycles and quantum heat engines. Phys. Rev. E, 76:031105,
Sep 2007.
[15] H. T. Quan, Y. D. Wang, Yu-xi Liu, C. P. Sun, and Franco Nori.
Maxwell’s demon assisted thermodynamic cycle in superconducting
quantum circuits. Phys. Rev. Lett., 97:180402, Oct 2006.
[16] H. T. Quan, P. Zhang, and C. P. Sun. Quantum heat engine with
multilevel quantum systems. Phys. Rev. E, 72:056110, Nov 2005.
[17] C. E. Shannon. A mathematical theory of communication. Bell System
Technical Journal, 27:379–423, Oct 1948.
[18] Kousuke Shizume. Heat generation required by information erasure.
Phys. Rev. E, 52:3495–3499, Oct 1995.
[19] V. Vedral. The role of relative entropy in quantum information theory.
Rev. Mod. Phys., 74:197–234, Mar 2002.