Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
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.
Keywords
Cite
@article{arxiv.2011.01286,
title = {Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)},
author = {Markus P. Mueller},
journal= {arXiv preprint arXiv:2011.01286},
year = {2021}
}
Comments
41 pages, 12 figures. V2: added hyperlinks to references; several minor corrections; new layout. V3, V4: corrected some typos and added some minor clarifications. Submitted to SciPost Lecture Notes. To appear in 'Quantum Information Machines; Lecture Notes of the Les Houches Summer School 2019', eds. M. Devoret, B. Huard, and I. Pop