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PHY2206H S specializedSpecial Topics QO II - Physics of Information and Quantum Communication Physics of Information and Quantum Communication

Course Title PHY2206H S specialized
Session spring
Year of Study 1st year
Time and Location Time: M-1pm T-10am
Location: MP1115
Course Homepage Link to Course Homepage

Hoi-Kwong  Lo


Official Description

 Part A:

1)      Reversible Computation and the Second Law of Thermodynamics

Reversible Computation: motivation, principle and limitations.

Moore’s law and energy cost in classical computations (theory and practice). Landaurer’s principle.  Maxwell’s demon and its resolution with information theory. Cost of erasure of information from the Second law of thermodynamics.

 2)       Entropy

The concept of entropy in Physics and Information Theory. Subjective (i.e. observer-dependent) nature of entropy. The resolution of Gibbs’ paradox from information theory.

 3)      von Neumman entropy and quantum computation

From classical (Shannon) entropy to quantum (von Neumann) entropy. Quantum computer as an ultimate reversible computer.

 4)      Carnot cycle in a Quantum World

 The smallest possible refrigerator.

 Part B: Quantum Communication:

1)      Basic concepts of quantum key distribution (QKD).

 2)      Protocols such as the Bennett-Brassard scheme, decoy state QKD and measurement-device-independent (MDI-QKD).

 3)      Fundamental limits to the rate of the distribution of entanglement and secure key rate over a quantum network.

Grading scheme:

 Assignment                           % of final grades           Date

Homework                              20%                             Throughout the course

Term Test                                40%                             Late March or early April                 Presentation and slides            40%                            Probably, during the last few lectures

 A 20-minute presentation will be made by each registered student. Students are welcome to propose tentative topics of their presentations and discuss them with the instructor well in advance. Students need to send a soft-copy of their presentation slides to the instructors immediately after their presentations. The grading will include the content and style of the presentation itself, the student’s performance during the Question and Answers session of his own presentation as well as others presentations. Also included in the marks will be the contents and presentation of the slides. Please notice that students’ participation in asking good questions during other students’ presentations will contribute to parts of the marks.



Prerequisite: Prior knowledge on the basics of classical thermodynamics (e.g. the Second Law of thermodynamics) is desirable, but not mandatory. Basic knowledge of quantum mechanics will be assumed.
Textbook For Part A:
1. Maxwell's Demon 2 Entropy, Classical and Quantum Information, Computing [Paperback], edited by Leff and Rex. Publisher: Taylor & Francis (first edition, 2002,
This edited book contains many original papers on topics such as reversible computation, Landaurer’s principle and Maxwell’s demon. (i.e Part A of the course).
2. Jaynes, E.T. (1996). "The Gibbs Paradox". pdf available as Reference 2 of
It discussed about the resolution of the Gibb’s paradox by noting that the very definition of entropy in statistical mechanics is observer-dependent because it depends on the observer’s state of knowledge and his/her available tools to manipulate a physical system. (i.e., Part B of the course).
3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press.
This introductory text covers topics on entropy, von Neumann entropy and quantum computation (i.e. Part C of the course).
4. N. Linden, S. Popescu, and P. Skrzypczyk, “How small can thermal machines be? The smallest possible refrigerator”, Phys. Rev. Lett. 105, 130401 (2010).
This paper concerns Part A4) of the course.
Other References:
5. J. Dunkel and S. Hilbert, “Consistent thermostatistics forbids negative absolute temperatures”, Nature Physics 10, 67 (2014).
This paper shows that negative absolute temperatures are strictly forbidden in thermodynamics and discusses about the subtleties in the definition of temperature in thermodynamics. It injects a note of caution in the discussion of how small thermal machines can be in Part D of the course.
For Part B:
A useful review paper is
1. “Quantum cryptography with realistic devices” Feihu Xu, Xiongfeng Ma. Qiang Zhang, Hoi-Kwong Lo, Jian-Wei Pan

Additional Notes


The first part of the course concerns the physics of information. We live in the Information Age. Information is physical as it must be represented by physical objects, which obey the laws of physics. Physics is informational as our ability to manipulate physical systems depends crucially on our state of knowledge. On one hand, the physics of information leads to interesting constraints on what is possible in information processing. On the other hand, the concept of information plays a crucial role in the understanding of fundamental laws in physics including the resolution of Maxwell’s demon and Gibb’s paradox. This course provides an introduction to the connection between physics and information.

 The second part of the course concerns the physics of quantum communication.

We will discuss about various protocols for quantum key distribution and the fundamental limits on the secure key rate.