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# 260047 VO Quantum correlations and generalized probabilistic theories: an introduction (2018W)

## Labels

## Registration/Deregistration

## Details

Language: English

### Examination dates

### Lecturers

### Classes

First lecture: Wed., October 3, 13:00 - 14:30.

All further lectures Wed., 14:15 - 15:45. Exception: no lecture on Dec. 5, instead extra lecture on Dec. 4, 17:15 - 18:45.

All lectures take place in the IQOQI Seminar Room, Boltzmanngasse 3,

## Information

### Aims, contents and method of the course

The goal of this lecture is to provide the theoretical foundations of the operational approach to quantum theory, which is the basis of Quantum Information Theory and the related research field of Quantum Foundations. The main emphasis is on correlations: quantum theory admits “stronger” correlations than classical physics (namely those that violate Bell inequalities), but, surprisingly, even stronger correlations are conceivable (so-called “PR box correlations”). We will first see how such correlations can be described mathematically, and how the violation of Bell inequalities can be used for technological applications (e.g. for the certification of randomness). Then we will see that quantum theory is only a special case of a larger class of generalized probabilistic theories (with physical properties different from quantum theory), and we will derive the Hilbert space formalism (with its operators, complex numbers etc.) from simple physical principles.

### Assessment and permitted materials

Oral exam at the end of the semester.

### Minimum requirements and assessment criteria

Successful exam, both regarding the content of the lecture notes as well as regarding the comprehension of the material gained by regular attendance.

### Examination topics

Basics of convex geometry, selected basics of quantum information theory (states, transformations, measurements), randomness versus no-signalling etc. More details during the lecture.

### Reading list

M. A. Nielsen and I. L. Chuang, Quantum Information and Quantum Computation (selected chapters), Cambridge University Press, 2010.

As an overview: S. Popescu, Nonlocality beyond quantum mechanics, Nature Physics 10, 264-270 (2014).

A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, 1982.

As an overview: S. Popescu, Nonlocality beyond quantum mechanics, Nature Physics 10, 264-270 (2014).

A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, 1982.

## Association in the course directory

MF 6, MaG 17, MaG 18, UF MA PHYS 01a, UF MA PHYS 01b

*Last modified: Mo 04.03.2019 15:28*