A derivation of quantum theory from physical requirements
- Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements-the principles of relativity and light speed invariance-are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.
Author details: | Lluis Masanes, Markus P. Müller |
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DOI: | https://doi.org/10.1088/1367-2630/13/6/063001 |
ISSN: | 1367-2630 |
Title of parent work (English): | New journal of physics : the open-access journal for physics |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/26 |
Volume: | 13 |
Issue: | 1 |
Number of pages: | 29 |
Funding institution: | Spanish MEC [FIS2008-00784, Consolider Ingenio 2010]; EU; Government of Canada through Industry Canada; Province of Ontario through the Ministry of Research and Innovation |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |
Publishing method: | Open Access |