260266 VO Advanced Quantum Information (2005W)

ECTS-points: 5
The set of lectures will present modern topics and problems of quantum information theory. This will be done as simple as possible, however without any over-simplifications. All derivations will only use the simplest required mathematics. More advanced and necessary mathematical notions will all be introduced during the lectures. The additional exercises are intended to be as interactive as possible.

The lecture will cover :
" The language of quantum mechanics:
o review of basic concepts and axioms
o introduction of the notations
" A formal description of entanglement, Schmidt decomposition and its generalizations.
" Structure of multi-qubit density matrices.
" Bell's theorem, and Bell's inequalities: assumptions, derivations, consequences.
" The GHZ paradox and its extensions.
" The Kochen-Specker theorem.
" Quantum informational processes and tasks:
o secret sharing
o communication complexity problems
o coin tossing
o secure communication
" Separability of density matrices. Entanglement of mixed states.
" Entanglement witnesses, and positive maps.
" Distillation of entanglement.
" Simple quantum algorithms.

In the exercises we will

" Solve to some specific problems related to the topics of the lectures
" Present and discuss some fundamental papers in which the basic ideas of quantum information were put forward
" Discuss some new entries in the quant-ph e-print archive (especially the most interesting ones which would appear in the archive during the period of the lectures)
" Point to new interesting papers, and discuss some open problems.