A Royal Road to Quantum Theory (or Thereabouts), Extended Abstract

Alexander Wilce
(Susquehanna University)

A representation of finite-dimensional probabilistic models in terms of formally real Jordan algebras is obtained, in a strikingly easy way, from simple assumptions. This provides a framework in which real, complex and quaternionic quantum mechanics can be treated on an equal footing, and allows some (but not too much) room for other alternatives. This is based on earlier work (arXiv:1206:2897), but the development here is further simplified, and also extended in several ways. I also discuss the possibilities for organizing probabilistic models, subject to the assumptions discussed here, into symmetric monoidal categories, showing that such a category will automatically have a dagger-compact structure. (Recent joint work with Howard Barnum and Matthew Graydon (arXiv:1507.06278) exhibits several categories of this kind.)

In Ross Duncan and Chris Heunen: Proceedings 13th International Conference on Quantum Physics and Logic (QPL 2016), Glasgow, Scotland, 6-10 June 2016, Electronic Proceedings in Theoretical Computer Science 236, pp. 245–254.
Published: 1st January 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.236.16 bibtex PDF

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