BCAM Course | Quantum information and entanglement theory for mathematicians
Date: Mon, Oct 23 - Fri, Oct 27 2023
Hour: 11:00 - 13:00
Location: Maryam Mirzakhani Seminar Room at BCAM and online
Speakers: Simon Morelli (BCAM)
Register: Registration Link
The goal of this course is to give an introduction to the rapidly growing field of quantum information theory. The course is aimed at a mathematical audience, but no knowledge of information theory or quantum mechanics is assumed.
This course starts with a short introduction to information theory, limited to concepts that will become relevant during the course, such as the definition of information in terms of Shannon entropy, and the theory of codes and channels. After this the postulates of quantum mechanics are introduced, where we define the state space and the states, the composition of multiple systems, the time evolution and quantum measurements. The last point will be of special interest and we will explain the concepts of projective measurements and non-commuting observables in more detail. After these fundamental theory terms like entanglement and nonlocality are explained in detail. Thereby we want to go a bit deeper into the subtleties of the theory and highlighting the potential of quantum systems for communication and computation. At the same time there also exist limitations that can be stated in terms of no-go theorems, such as the no-cloning theorem crucial to not allow faster than light communication. Applications of entanglement and non-locality include quantum teleportation, dense coding and secure quantum cryptography. If time allows, also the advantages and difficulties of quantum computation will be discussed.
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