QUANTUM INFORMATION

The course provides an introduction to the fundamental concepts of both classical and quantum information theory. The approach will be simple yet rigorous. The first part of the course will cover fundamental results such as the source coding theorem, data compression, and channel capacity. The course does not include programming modules.

General educational objectives in terms of expected learning outcomes:

• Knowledge and understanding: Students will gain an in-depth understanding of the fundamental concepts of information theory, including entropy, redundancy, channel capacity, source and channel coding, and Shannon’s theorems. They will understand the application of these concepts in various contexts, such as data compression, cryptography, and digital communications.
• Applying knowledge and understanding: Students will be able to apply the principles and techniques of information theory to solve problems in the fields of data transmission, signal processing, and communications. They will be able to design data compression algorithms and analyze the performance of communication systems.
• Making judgements: Students will develop the ability to critically analyze problems related to information theory, assess the effectiveness of different algorithmic and technical solutions, and justify design choices based on theoretical and practical criteria.
• Communication skills: Students will be able to effectively communicate concepts, methods, and results of information theory to both specialists and non-specialists through oral and written presentations, technical reports, and the appropriate use of mathematical and formal languages.
• Learning skills: Students will acquire the skills necessary for continuous and independent learning in information theory and related fields. They will be able to update their knowledge and skills through research, critical analysis of scientific literature, and practical application of the concepts learned.

Lecture-based. 

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

GENERAL COURSE DESCRIPTION

The course offers an introduction to classical and quantum information theory.

COURSE CONTENTS

PART 1: Classical Information

• Elements of classical information theory
• Basics of probability
• Entropy, Mutual Information, and related functions
• Source coding theorem
• Data compression. Block codes and code length limits
• Channel capacity

PART 2: Quantum Information

• Preliminary concepts and notation
• Quantum states, measurements, and channels
• Quantum noise
• Quantum computational complexity

(1) John Watrous. The Theory of Quantum Information, Cambridge University Press, 2018

(2) N. David Mermin. Quantum Computer Science - An Introduction (5th edition), 2016

(3)  Sanjeev Arora and Boaz Barak. Computational Complexity: A Modern Approach, Princeton University, 2006 (only for the complexity part)

The exam consists of a written test and an oral interview. The written test typically consists of open-ended questions.
To pass the written test, a score of at least 18 is required. The written test can be reviewed before taking the oral exam.

Midterm assessments: It is possible to take multiple midterm tests. The first test usually covers classical information theory. The second and third tests will cover quantum information.

The assessment may also be conducted remotely if conditions require it.

Grades are assigned according to the following scheme:

• Not passed: The student has not acquired the basic concepts and is unable to answer at least 60% of the questions or solve theoretical and practical exercises.
• 18-20: The student demonstrates barely sufficient mastery of the basic concepts and/or struggles to approach theoretical/practical exercises, making several mistakes.
• 21-24: The student demonstrates a minimal understanding of the basic concepts, has limited ability to connect the course contents, and can solve simple exercises.
• 25-27: The student demonstrates good mastery of the course content, has a good ability to link the course concepts, and solves exercises with few errors.
• 28-30 e lode: The student has fully mastered all course content, can critically connect the concepts, and solves the exercises completely and without significant errors.

Theoretical exercises (e.g., on the properties of entropy). Various types of exercises on data compression, entropy, and the various concepts studied in class.                              

Exercises regarding the representation of qubit states, their normalization, and fundamental properties. Exercises in constructing states of multi-qubit systems through tensor products and analyzing the resulting states. Exercises to study the properties of entangled states, such as Bell states, and the analysis of state non-separability. Exercises on quantifying entanglement. Theoretical exercises to demonstrate the impossibility of cloning arbitrary quantum states and its implications. Exercises in calculating the von Neumann entropy for mixed states and analyzing information loss.