## John-von-Neumann Lecture: Quantum Non-Locality: A Mathematical Perspective [MA5030]

### Sommersemester 2014

Start on Tuesday, May 6, 2014.
Prerequisites (recommended): Students are supposed to have a Bachelor degree in Mathematics, Physics or Computer Science.
There is no need to know anything about quantum mechanics or functional analysis.

Intended Learning Outcomes: After successful completion of the module, students will know the basics of operator spaces and tensor norms and understand why this is the natural framework to study quantum non-locality. Students will understand the meaning and implications of the notion of non-locality and why it naturally leads to applications in different areas of physics and computer science.

Content: The course discusses quantum non-locality, one of the most relevant features of quantum mechanics. The concept of non-locality goes back to the famous Einstein-Podolsky-Rosen criticism in the 30's and nowadays lies at the core of the application of quantum mechanics in cryptography. The course is focused on the use of functional analysis tools in this context: operator spaces and tensor norms.

The course is modular to try to cover the different backgrounds and interests of students and researchers at TUM.
It consists of an introduction, two background modules as a pre-course, a core module and three independent modules to cover different areas of interest.

- Module 0: Introduction and motivation.
- Module 1(pre-course): Basics in quantum mechanics.
- Module 2 (pre-course): Basics in functional analysis.
- Module 3 (core module): Operator spaces and tensor norms.
- Module 4: Non-locality in foundations of quantum mechanics.
- Module 5: Non-locality in complexity theory.
- Module 6: Non-locality in cryptography

Teaching and Learning Methods: Lectures. Exercises.

Lecture notes:

Reading List:

- G. Pisier, Introduction to Operator Space Theory, Cambridge University Press, 2003.
- H. Buhrman, R. Cleve, S. Massar, R. de Wolf, Nonlocality and communication complexity, Rev. Mod. Phys. 82, 665-698 (2010).
- M. Junge, C. Palazuelos, Large violation of Bell inequalities with low entanglement, Comm. Math. Phys. 306, 695-746 (2011).
- M. Junge, C. Palazuelos, D. Perez-Garcia, I. Villanueva, M.M. Wolf, Operator spaces: a natural framework for Bell inequalities, Phys. Rev. Lett. 104, 170405 (2010).