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.

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