- Understanding that the world is fundamentally completely quantum.
- Precise understanding of the four axioms of quantum theory
- Knowledge of the complete mathematics needed to understand quantum systems (with pure spin degrees of freedom, which means without translational degrees of freedom).
- Conceptual and technical grasp of state spaces of quantum systems
- Conceptual and technical grasp of quantum measurement predictions
- Conceptual and technical grasp of unitary and projective dynamics.
- Conceptual and technical grasp of how quantum systems are composed.
- Ability to apply the theory to prototypical quantum systems
- Precise understanding of quantum teleportation, cryptography, etc.
This course presents a complete and self-contained explanation of what it really means that all matter is quantum. No prior knowledge of physics is required or even desirable. After an opening tour d’horizon, the first part of the course consists in a thorough exposition of the mathematics that is needed for a complete understanding of quantum systems. The second part will then introduce and discuss the four physical axioms of quantum mechanics in their complete and precise formulation and thus establish our state-ofthe- art conceptualization of the physical world. The third part will then consist in the application of these axioms to prototypical quantum systems and indeed contemporary high-tech applications such as quantum teleportation, quantum cryptography and quantum computing.|
Without loss of conceptual generality, we restrict our attention to pure spin systems, which one may think of as matter that cannot move in space. While this restriction removes many mathematical subtleties that would otherwise require years of prior study, it does not result in any reduction of the complexity of quantum theory. The dedicated student will thus get to know all conceptual aspects of quantum mechanics and master all required techniques.
Written presentation of particular topics and/or oral examination of the core material.