Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)

• URL: http://arxiv.org/abs/2011.01286v4
• Date: Tue, 30 Mar 2021 12:30:03 GMT
• Title: Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
• Authors: Markus P. Mueller
• Abstract summary: These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) I present two conceivable phenomena beyond quantum: superstrong nonlocality and higher-order interference. I summarize a reconstruction of quantum theory from the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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