Seminar (WS 2025/26)

Mathematical fundamentals of quantum statistics

Preliminary discussion:

t.b.a.

Registration:

Please register for the seminar by using MÜSLI.

Time and location of the seminar:

The seminar will be held as a Blockseminar on two days in January 2025.

Contact:

Henning Stein <henning.stein[at]math.uni-heidelberg.de>

Jan JOHANNES <johannes[at]math.uni-heidelberg.de>

Questions, please directly by email.

Language:

The seminar will be in Englishh, if there is at least one non-German speaking participant.

Field:

Applied Mathematics, Stochastics

Description of the seminar:

The axioms of quantum mechanics as formulated by John von Neumann give a mathematical description of quantum systems. The objects arising are inherently random and this randomness is fundamentally different than the one described by classical probability theory. This seminar studies quantum statistics from a mathematical point of view where quantum systems are described by positive trace-class operators on a separable complex Hilbert space. Systems can only be observed using measurements which have a randomized outcome and alter the system drastically. While many of the concepts of classical statistics can be generalized to the quantum setting, many quantum phenomena are unparalleled in classical statistics.

Possible presentation topics:

t.b.a.

 

Each participant is expected to give a 60 minutes. A handout containing the most important definitions and results as well as short sketches of the proofs should be prepared for the other participants.

Requirements:

The seminar is for advanced Master students who want to specialize in statistics and are already familiar with the topics typically covered in the lectures Probability Theory I, Statistics I and Functional Analysis.

References:

(1) Stéphane Attal: Lectures in Quantum Noise Theory

(2) Alexander Holevo: Probabilistic and Statistical Aspects of Quantum Theory

(3) Michael Nielsen, Isaac Chuang: Quantum Computation and Quantum Information