Time and Venue: Lectures will be held on Mondays, Wednesdays and Fridays at 11am in MR11.

Description: This course will start with a short introduction to some of the basic concepts and tools of Classical Information theory, which will prove useful in the study of Quantum Information Theory. Topics in this part of the course will include a brief discussion of data compression, transmission of data through noisy channels, Shannon's theorems, entropy and channel capacity. Classical error-correcting codes will be discussed, with a special emphasis on linear codes. The knowledge of the latter will be useful for the study of quantum error correcting codes (which are by definition linear).

The quantum part of the course will commence with a study of open systems and a discussion of how they necessitate a generalization of the basic postulates of Quantum Mechanics. Topics will include quantum states, quantum operations, generalized measurements, POVM and the Kraus Representation Theorem. Entanglement and some applications elucidating its usefulness as a resource in Quantum Information Theory will be discussed. The concept of quantum error correction will be introduced and various examples will be discussed in detail. This will be followed by a study of the von Neumann entropy and its interpretation as the data compression limit of a quantum information source. Schumacher's theorem will be discussed in detail. Various examples of quantum channels will be introduced and capacities of quantum channels will be discussed.

Desirable Previous Knowledge: Basic knowledge of the postulates of Quantum Mechanics, as summarised in the prerequisites, will be assumed. However, an additional lecture could be arranged for students who do not have the necessary background in Quantum Mechanics. Elementary knowledge of Probability Theory, Vector Spaces and Group Theory will be useful. Students who have attended the Part III Information and Coding course and/or a previous course in Quantum Mechanics will be at an advantage, but this will not be considered as a pre-requisite. It will be helpful for students to attend the course on Introduction to Quantum Computation (lectured in the Michaelmas Term).

Lecturer: Nilanjana Datta

Class Instructors: Nilanjana Datta

Example Classes: (example sheets distributed in class)

• Class 1:
• Class 2:
• Class 3:
• Class 4:

Textbooks:

• Quantum Computation and Quantum Information by M.A. Nielsen and I.L. Chuang (CUP)
• Quantum Computing by Jozef Gruska (McGraw Hill)
• Classical and quantum computation by A.Yu. Kitaev, A.H. Shen and N.N. Vyalyi (AMS)
• Elements of Information Theory by T.M.Cover and J.M.Thomas (Wiley & Sons)
• John Preskill's lecture notes on Quantum Computation

• Prerequisites
• Lecture 1
• Lectures 2 & 3
• Lecture 4
• Lectures 5 and 6
• Lecture 7
• Lecture 8
• Lecture 9 and 10
• Lecture 11 - 13
• Lecture 14 and 15
• Lecture 16 and 17
• Lecture 18
• Lecture 19
• Lecture 20
• Lecture 21 and 22
• Lecture 23

(distributed in class)

• Example Sheet 1
• Example Sheet 1