Quantum Information Theory

Quantum Information is the study of how the principles of quantum mechanics can be harnessed to process, transmit, and store information in fundamentally different ways from classical systems. By utilizing uniquely quantum phenomena such as superposition and entanglement, Quantum Information allows for tasks like faster computation and more secure communication, offering capabilities that are impossible in the classical world. The field bridges foundational questions about quantum theory with practical applications in technology, making it both a theoretical and applied science.

While other courses at ULB (INFO-H514 and INFO-H517) primarily focus on “how” quantum effects can be exploited to perform computational or information tasks, this course focuses on the “why” of quantum information, examining the underlying principles that allow quantum theory to achieve such effects. It is geared toward physicists who seek a deeper understanding of the fundamental aspects of quantum theory, rather than just its applications in computation or cryptography.

Historically, there has been a rich and fruitful interplay between the foundations of quantum theory and quantum information science. In this course, we will dive into some of the foundational questions and puzzles that have shaped both fields. We will review key quantum phenomena such as interference, the no-cloning theorem, quantum teleportation, and non-locality and present important no-go theorems such as Bell's theorem and the PBR theorem. We will also introduce the major interpretations of quantum mechanics, including many-worlds, de Broglie-Bohm theory, and collapse models, as well as the operational perspective of quantum mechanics, framing it in the context of generalized probabilistic theories.

A central focus of the course is entanglement, a resource that underpins many of the advantages of quantum information processing. We will introduce the resource theory of entanglement, examine its role in quantum computation and many-body physics, and discuss how systems with low entanglement can be efficiently simulated using tensor-network states. Additionally, we will explore Bell's non-locality and its role in self-testing and device-independent quantum information theory.

Although this course can be taken independently of PHYS341, students interested in quantum information are encouraged to take both courses for a more comprehensive understanding of the field.

The objective of this course is to provide students with a deeper understanding of the foundational principles of quantum mechanics and their role in quantum information theory. Students will explore key concepts like entanglement, non-locality, and quantum interpretations, gaining insight into the theoretical underpinnings that make quantum information possible.

Required and Corequired knowledge and skills

Quantum theory, Dirac notation, Linear Algebra (vector spaces, eigenvalues, eigenvectors, matrix operations), probability theory.

Lectures at the blackboard and/or using projected presentations.

Contribution to the teaching profile

This course enhances the teaching profile by offering an in-depth exploration of the foundational aspects of quantum theory and quantum information, complementing more application-focused courses. It broadens the curriculum by addressing key concepts like entanglement and non-locality.

References, bibliography, and recommended reading

See page of the course on Université Virtuelle

Contacts

Stefano Pironio (stefano.pironio@ulb.be)

Campus

Plaine

Method(s) of evaluation

• Oral examination
• Oral presentation

Oral examination

• Open book examination
• Examination with preparation

Oral presentation

Language(s) of evaluation

• english