# The closest cousins of quantum theory from three simple principles

### APA

Ududec, C. (2012). The closest cousins of quantum theory from three simple principles. Perimeter Institute. https://pirsa.org/12080007

### MLA

Ududec, Cozmin. The closest cousins of quantum theory from three simple principles. Perimeter Institute, Aug. 07, 2012, https://pirsa.org/12080007

### BibTex

@misc{ pirsa_PIRSA:12080007, doi = {10.48660/12080007}, url = {https://pirsa.org/12080007}, author = {Ududec, Cozmin}, keywords = {Mathematical physics}, language = {en}, title = {The closest cousins of quantum theory from three simple principles}, publisher = {Perimeter Institute}, year = {2012}, month = {aug}, note = {PIRSA:12080007 see, \url{https://pirsa.org}} }

Government of the United Kingdom

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Talk Type

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Abstract

A very general way of describing the abstract structure of quantum theory is to say that the set of observables on a quantum system form a C*-algebra. A natural question is then, why should this be the case - why can observables be added and multiplied together to form any algebra, let alone of the special C* variety? I will present recent work with Markus Mueller and Howard Barnum, showing that the closest algebraic cousins to standard quantum theory, namely the Jordan-algebras, can be characterized by three principles having an informational ﬂavour, namely: (1) a generalized spectral decomposition, (2) a high degree of symmetry, and (3) a requirement on conditioning on the results of observations. I'll then discuss alternatives to the third principle, as well as the possibility of dropping it as a way of searching for natural post-quantum theories.