Quantum entanglement 2023 spring

Introductory lectures on quantum entanglement, to physicist (BSc,) MSc, and PhD students.
The main purpose is to illustrate quantum entanglement in finite dimensional Hilbert spaces, where the abstract notions can be made explicit by using geometric approach.
Recommended prerequisite: linear algebra. Useful prerequisite: quantum mechanics; however, the course is also useful alongside the regular quantum mechanics course, it gives a different point of view.

The physical systems in nature show different behavior in small and large scales, called "quantum" and "classical", respectively. The characteristic trait of the quantum behavior is a remarkable type of correlation, called entanglement. There is no entanglement in classical systems, which are described by classical probability theory. Entanglement in quantum systems, although being a simple consequence of the quantum superposition principle, is a long-standing challenge for the classically thinking mind. Besides the practical applications, the investigation of quantum entanglement and quantum correlations in general represents a highly important point of view to understand the differences between classical and quantum physics. It might be interesting to learn about a generalized probability theory also for mathematician students.

Teaser (in Hungarian): Szalay Szilárd, Kvantumkorrelációk és rejtett változók (ismeretterjesztő cikk kvantumkorrelációkról, megjelent a Fizikai Szemle (ELFT) LXXIII. évfolyamának 1. számában (2023/01))

Topics planned to be covered:

Course Information

Information, announcements


There is an exercise sheet updated week-by-week, following the topics of the lectures, for the interested attendants. There is no submission, although we may consult; there is no deadline, although it is helpful to consider the exercises alongside the lectures, as they deepen and illustrate the material.

Recommended texts

The material of the course comes from several sources, including also research articles. There is no single textbook containing all that, so taking notes is recommended. Below there are some important, comprehensive works, giving wide overviews, far beyond the scope of the course. First, some general textbooks for the preliminaries:

Then, to the actual material of the course:

Some mathematical tools:

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