Operator Algebraic Tools in Quantum Information Theory
Time: Tuesday 4-5.30 pm Wednesday 4-5.30 pm
Location: 03.06.011/ 02.10.011 Instructor: Marius
focus of this course lies in information theoretical foundations based
on common tools from functional analysis. The major gools are on
entropic inequatities including
Additivity of squashed entanglement
Decay for semigroups
Quantum mechanics and simple norms
Entropy, weak typicality, and channels
Relative entropy, minimal output entropy for classical channel
Classical Data processing inequality
concepts in mathematics have been
developped to understand solutions, and solutions spaces of certain
PDE's. This allows to classify and treat certain classes of PDE's.
Fourier analysis is one the most of important of these theories. In
this sense this couse is also a first step towards mathematics on the
I: Basics on PDE's
What is a PDE? Linear PDE's, characteristic curves and lines,
II Wave equation
to find a solution in 1D? causality, solution formulae, reflection
principle, inhomogenous problem (3.3-3.4), well-posedness.
III Fourier analysis
spaces and inner products, abstract Fourier coefficients,
concrete Fourier coefficients, different form of convergence,
Gibbs phenomena, a little peek at continuous Fourier coefficients.
IV Heat equation
Solution formulae, reflection, source, well-posedness.
V Boundary problems in 1D
separation of variables.
VI Laplace equation
The equation, rectangles and cubes, Poisson formula
VII Boundary problems in plane and space
solid virbration, Legendre functions.
Walter A. Strauss, Partial Differential Equations, An Introduction, Second edition
Attendance: If you
miss the class more than three times unexcused, you may be dropped! It
is you task to drop the class in time, and make space who actually need
the class. If I can not recognize a student, he will not be
handed out an exam.
Link to lectures
Homework (20%)Practice probems
Midterm1 January 31 (25%)
Midterm2 February 28 (25%)
Final (7:00-10:00 p.m., Wednesday, May 9) (30%)
Practice probems solutions
Practice problems final
Practice problems final solutions
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