Topics Between brackets estimated nr of lectures 1 Advanced linear algebra (4) (Petz, Fannes) 2 Quantum mechanics (6) (Werner, Maassen) 3 Quantum statistical mechanics (3) (Alicki, Benatti) 4 Classical information (4)(R. Gill, Y. Suhov) 5.1 Quantum information 1 (3) (Winter) 5.2 Quantum information 2 (3) (Holevo) 6 Practical implementation (4)(Buchleitner, M. Genovese (Torino) or S. Kulik (Moskow)) 7 Quantum cryptography (3) (Bruess, Petritis) 1 Orthogonal spaces, matrices over C eigenvalues, singular values, Jordan direct sums, tensor products, Schmidt decomposition convexity states and discrete probability GNS 2 quantum vs classical phenomena (Ising spin vs spin 1/2) description of isolated systems, mean values, probabilities, dynamics, measurements, von Neumann entropy multi-partite systems and partial operations positivity, complete positivity, unitary dilations 3 quantum statistical systems, spin systems, Fermi, Bose, coherent states equilibrium states, KMS translation invariant states, mean entropy 4 sources and channels stochastic processes, Bernoulli, Markov entropy, relative entropy information, conditional information, mutual information codes and noiseless compression (Shannon 1) noisy channels, capacity (Shannon 2) 5.1 Bell's states, dense coding, quantum teleportation witnessing entanglement: Bell's inequalities, positive maps measuring entanglement, distillation and formation of mixed entanglement 5.2 quantum stochastic processes quantum noiseless compression quantum capacities and additivity questions 6 state reconstruction, quantum tomography quantum optics Mach-Zender interferometer beam splitters, squeezers, parametric down conversion atom interferometers Bose-Einstein condensates 7 Quantum Cryptography probabilistic classical cryptography (Vernam's code; estimate of its average deciphering time) classical solution of the key distribution problem (RSA algorithm) no cloning theorem quantum solution of the key distribution problem (BB84, BB92, EPR algorithms) 8 Experimental Implementations state reconstruction, quantum tomography quantum optics Mach-Zender interferometer beam splitters, squeezers, parametric down conversion atom interferometers Bose-Einstein condensates