FYSJ5108 PH1: Impossible Quantum Machines and their Optimal Approximations (JSS34) (2 op)

It is well known that it is possible to clarify the conceptual basis of quantum mechanics and the well-known limitations it poses through a hierarchy of impossible machines. The aim of this mini-course is to present this approach and illustrate how it is possible to apply the theory of finite group representations to realise an approximate version of such impossible devices.

The lectures include:
- elements of group representation theory
- description of impossible machines (universal cloner, universal joint measurement, universal sequential measurement)
- quantum information theoretic description of possible machines
- impossibility proofs
- explanation of approximative scenarios
- group theoretic method to construct optimal devices

1) basic understanding of conceptual limitations imposed by quantum theory
2) basic understanding of group theoretic strategies in the realization of approximate devices

Analysis, linear algebra, basics of quantum theory