Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
arXiv:2011.01286 · doi:10.21468/SciPostPhysLectNotes.28
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.
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
References in corpus (11)
- Quantum Mechanics as Quantum Information (and only a little more)
- Characterizing quantum theory in terms of information-theoretic constraints
- Private Randomness Expansion With Untrusted Devices
- A derivation of quantum theory from physical requirements
- A generalized no-broadcasting theorem
- Almost quantum correlations
- Higher-order interference and single-system postulates characterizing quantum theory
- Tsirelson's Problem
- Measurement sharpness cuts nonlocality and contextuality in every physical theory
- Quantum theory from rules on information acquisition
- Strongly symmetric spectral convex bodies are Jordan algebra state spaces