Quantum Information

Academic Year 2025/2026 - Teacher: DARIO CATALANO

Expected Learning Outcomes

This class teaches the basics of information theory and modern cryptography in an accessible yet rigorous manner. The first part of the course focuses on some foundamental results in information theory such as the source coding theorem, data compression and channel capacity.

Learning objectives

1. Knowledge and Understanding: Students will gain a deep 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.

2. Applying Knowledge and Understanding: Students will be able to apply the principles and techniques of information theory to solve complex problems in the fields of data transmission, signal processing, and communications. They will be capable of designing data compression algorithms and analyzing the performance of communication systems.

3. Critical Judgment Skills: Students will develop the ability to critically analyze problems related to information theory, evaluate the effectiveness of different algorithmic and technical solutions, and justify design choices based on theoretical and practical criteria.

4. Communication: 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 use of appropriate mathematical and formal languages.

5. Learning Skills: Students will acquire the necessary skills for continuous and autonomous 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.

Course Structure

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.

Required Prerequisites

Linear Algebra and Discrete math basics

Attendance of Lessons

Attenting classes is not mandatory but strongly recommended.

Detailed Course Content

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 key results such as the source coding theorem, data compression, and channel capacity. The course does not include programming modules.

Course Planning

	Subjects	Text References
1	Probability basics	Cap 2 di [1]
2	Entropy, Mutual Information	Cap 3 di [1]
3	The Source Coding Theorem	Cap 4 di [1]
4	Data Compression. Codes and their length	Cap 5 di [1]
5	Channel Capacity	Cap. 9 di [1]
6	The probabilistic model; Quantum bits, Unitary operations, and measurements.	Cap 1 di [3]
7	Multiple quantum bit systems; Tensor products; Dirac notation; Density matrices; Operations on density matrices	Cap 2 di [3]
8	Density matrices; Operations on density matrices; Partial trace.	Cap 2 di [3]
9	Quantum measurement; Quantum channelsInformation-complete measurements; Partial measurements.	Cap 2 di [3]
10	Purifications; Schmidt decomposition; Von Neumann entropy; Quantum compression.	Cap 3 e 5 di [3]
11	The Bloch sphere; Hamiltonians; The No-cloning theorem.	Cap 2 di [4]
12	Quantum Teleportation; Entanglement swapping; The GHZ state; Monogamy of entanglement.	Cap 6 di [4]
13	Quantum error correction; Shor's 9 qubits code; Quantum Fault Tolerance.	Cap 5 e Appendix N di [4]
14	Quantum computational complexity: Promise problems and complexity classes; Quantum complexity classes (Uniform Circuits, BQP, Quantum proofs: QMA).	Cap 20 di [5]

Learning Assessment

Learning Assessment Procedures

The exam consists of a written test and an oral interview. The written test typically includes open-ended questions and must be passed with a minimum score of 18/30. Students may review the written test before the oral exam.

In-course Tests: Multiple in-course assessments may be held, with the first typically covering classical information theory. Assessments may also be conducted online if necessary.

Registration: Students must register for the final exam via the SmartEdu portal. For technical issues, contact the Academic Office.

Accommodations: Students with disabilities or specific learning disorders (DSA) should notify the instructor and the DMI CInAP representative well in advance to arrange appropriate accommodations.

Grading Scale:

Fail: The student has not acquired basic concepts and cannot answer at least 60% of questions or complete exercises.
18–20: Sufficient mastery of basic concepts; exercises completed with difficulty and errors.
21–24: Minimal mastery of concepts; can solve simple exercises and make basic connections.
25–27: Good mastery of content; solves exercises with few errors and demonstrates solid understanding.
28–30 cum laude: Excellent mastery of all course content; demonstrates critical thinking and solves exercises completely and accurately.

Examples of frequently asked questions and / or exercises

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.

VERSIONE IN ITALIANO

Degree Course in

Computer Science