Master in Theoretical Physics and Applications

This is a collection of classroom documents for the two courses I am teaching at international Master in Theoretical Physics and Applications :

Introduction to Dynamical Systems

Exercices:

Bibliography:

  • Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics), by Stephen Wiggins – Springer
  • Chaos: An Introduction to Dynamical Systems, by Kathleen T. Alligood, Tim D. Sauer, James A. Yorke – ISBN-13: 978-0387946771
  • Chaos and nonlinear dynamics an introduction for scientists and engineers, by Robert Hilborn – ISBN-13: 978-0198507239

Quantum Information Theory

  • Introduction :
      quantum information vs classical information ;
      quantum complexity ;
      physical implementation.
  • Qu-bits and density matrices:
      definition,
      Bloch sphere,
      Gleason theorem.
  • Entanglement:
      EPR pairs and hidden information,
      Bell inequalities.
      Application to the quantum teleportation
  • Measurement:
      orthogonal measurement,
      POVM,
      complete positivity.
  • Quantum algorithms:
      complexity classes
      Grover algorithm
      factoring
  • Quantum error correcting codes:
      depolarizing channel
      CSS codes
      Some useful bounds
      Stabilizer codes.