Prof. Valerio Scarani
Centre for Quantum Technologies and Department of Physics
National University of Singapore
physvnus.edu.sg

Contents (version 1)

These lectures are meant as a general introduction to quantum physics and quantum information. The description of physical systems is rarely discussed in classical physics, and when it is, one rapidly understands that such a description is trivial. However, since the advent of atomic physics, many phenomena have been observed that cannot be accounted for if systems are described in the trivial classical way. After substantiating this "negative" statement, I shall present its "positive" counterpart: quantum physics is a description that goes beyond the classical one and that, as of today, describes all observed phenomena in a convenient way.

1 Quantum physics
1.1 The description of physical systems
1.2 Axioms, assumption and theorems
1.2.1 Kinematics: Hilbert space
1.2.2 Dynamics: reversibility
1.2.3 Case study of axiomatics: Jauch-Piron
1.3 Tutorials

2 Entanglement
2.1 Tensor product algebra
2.2 Partial trace and no-signaling
2.3 Case study: the singlet state
2.4 A note on decoherence
2.5 Tutorials

3 Two primitives of quantum information
3.1 Quantum cloning
3.1.1 The no-cloning theorem
3.1.2 Optimal cloning
3.2 Teleportation
3.3 Tutorials

4 The failure of alternative descriptions
4.1 Local hidden variables
4.2 Superluminal communication
4.2.1 Bounds on the speed in a preferred frame
4.2.2 Before-before arrangement in the local frames
4.3 Leggett’s model
4.4 Tutorials

5 The mathematics of no-signaling
5.1 The question of Popescu and Rohrlich
5.2 Polytopes: a case study
5.3 The question revisited: why 2\sqrt{2}?
5.4 Tutorials

6 The power of Bell
6.1 Device-independent quantum cryptography
6.2 Black-box source tomography
6.3 Guaranteed randomness
6.4 Tutorials