## Probabilistic theories and reconstructions of quantum theory

Markus P. Müller

SciPost Phys. Lect. Notes 28 (2021) · published 31 March 2021

*Part of the 2019-07: Quantum Information Machines Collection in the Les Houches Summer School Lecture Notes Series.*

- doi: 10.21468/SciPostPhysLectNotes.28
- Submissions/Reports

### Abstract

These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how physics could be even more general than quantum, I present two conceivable phenomena beyond QT: superstrong nonlocality and higher-order interference. Then I introduce the framework of GPTs, generalizing both quantum and classical probability theory. Finally, I summarize a reconstruction of QT from the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom. In particular, I show why a quantum bit is described by a Bloch ball, why it is three-dimensional, and how one obtains the complex numbers and operators of the usual representation of QT.

### Cited by 18

### Author / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Markus Müller

^{1}Perimeter Institute [PI]^{2}Institut für Quantenoptik und Quanteninformation Wien / Institute for Quantum Optics and Quantum Information Vienna [IQOQI Vienna]

- Gouvernement du Canada / Government of Canada
- Ministry of Research and Innovation (Canada, Ontario, Min Res&Innov) (through Organization: Ministry of Research, Innovation and Science - Ontario [MRIS])