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