Introduction to quantum information theory

1. States: Density matrices, Inner product, Norms, Fidelity, TVD, State decomposition (Schmidt, Pauli)  

2. Operators (1): Unitary representation, CPTP Maps, Other representations (larger unitary / Kraus / Choi) 

3. Operators (2): Pauli operators, Channels acting on operator algebra, Recovering subsystems from commutation relations, Clifford Hierarchy, Classes of restricted operations (LOCC, LO1WCC)  

4. Measurements: Projective Measurements, Update rule, POVM, Non-commuting / joint measurability   

5. Entanglement: Measures of entanglement, Entanglement monotones, Distillation of entanglement, Using entanglement (Teleportation, Swaping, Gate teleportation, Relation with Choi, Super dense coding)  

6. State discrimination: Hypothesis testing, Entropies, Holevo, Conditional entropy / mutual information / strong subadditivity, Data processing inequality, Relative Entropy, Pinsker   

7. State estimation: Tomography, Efficiency of tomography, Shadow Estimation  

8. Some applications of quantum communication: QKD, Fingerprinting, Uncloneable encryption, Self-testing