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- The closest cousins of quantum theory from three simple principles

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12080007

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.

©2012 Perimeter Institute for Theoretical Physics