Introduction to Quantum Information Theory

Professor: Dr. Gustavo Martin Bosyk (Contact: gbosyk@gmail.com).

Hours: 22hs.

Chronogram: 11 lessons of 2hs. Starting on 3 March, 2021 and continues every Wednesday until 12 May, 2021.

Short description and program: The subject of the course is the Quantum Information Theory, an interdisciplinary area that has acquired an extraordinary development in the last decades. Quantum Information Science essentially investigates on the potential of Quantum Mechanics to generate radically new forms of transmission, storage and processing of the information. This is an introductory course and it is oriented to the physical and mathematical aspects of the mentioned topics. Students from Physics, Mathematics, Computer Science, Engineer, Philosophy of Science, as well as, any interested in the Quantum realm are welcome. Prior knowledge of Quantum Mechanics and Linear Algebra is helpful, but not required. The main aim of the course is to introduce to the students with the new concepts and methods of Quantum Information Theory, which play a very important role in various areas of current Physics.

The program of the course is as follows:

Part 1: Foundations of Quantum Mechanics. Review of mathematical formalism (Dirac bra-ket notation). Postulates of quantum mechanics. Quantum states: pure and mixed states. Geometry of Quantum Bits: Bloch sphere. Observables: complementarity and uncertainty. Measurements: projective and generalized measurement. Probabilities: Born's rule.

Part 2: Composite systems. Global and reduced density operator. Partial trace. Schmidt decomposition. Purification. LOCC paradigm. Definition of inseparability for pure and mixed states. Quantum entanglement measures. Implications and applications of quantum entanglement. Bell inequalities. Separability criteria for non-pure states. Partial positive transposition. Classical and Quantum Correlations: Quantum Discord.

Part 3: Basics of Quantum Computing. Basics Quantum Circuits. Matrix representation of basic operations. Universal quantum gates. Quantum Algorithms (Quantum Teleportation, super dense coding, Grover’s search algorithm, etc).