Course content :

1. Open quantum systems

Module 1: E.M. field quantization, basic elements of quantum optics

Module 2: States of atoms, Jaynes-Cummings Hamiltonian, elementary quantum gates

Module 3: Open-quantum systems and quantum measurements

Module 4: Quantum state and process tomography

2. Formalism of quantum information dynamics

Module 5: States and quantum phases of matter, formal theorems on unitary constructions.

Module 6: Classes and properties of entanglement entropy, applications to many-body systems.

Module 7 : Quantum thermalization (ETH, trace distance).

Module 8 : Area laws vs. volume laws of entanglement.

3. Applications: Gravity, cryptography, mesoscopic systems

Module 9 : Entanglement entropy in gravity.

Module 10 : Quantum algorithms, topological quantum computing and error correction.

Module 11 : Basics of quantum cryptography and mesoscopic quantum information.

Module 12 : Open directions, various physical systems.