2017/01/03 by Alexander Wilce
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.3390/e20040227
published as EPTCS 236, 2017, pp. 245-254 · In Proceedings QPL 2016, arXiv:1701.00242
arxiv created 2017/01/03 · arxiv updated 2018/05/09
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.)