# Three ways to classicalize (nearly) any probabilistic theory

### APA

Wilce, A. (2021). Three ways to classicalize (nearly) any probabilistic theory. Perimeter Institute. https://pirsa.org/21060086

### MLA

Wilce, Alexander. Three ways to classicalize (nearly) any probabilistic theory. Perimeter Institute, Jun. 11, 2021, https://pirsa.org/21060086

### BibTex

@misc{ pirsa_PIRSA:21060086, doi = {10.48660/21060086}, url = {https://pirsa.org/21060086}, author = {Wilce, Alexander}, keywords = {Quantum Foundations}, language = {en}, title = {Three ways to classicalize (nearly) any probabilistic theory}, publisher = {Perimeter Institute}, year = {2021}, month = {jun}, note = {PIRSA:21060086 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

It is commonplace that quantum theory can be viewed as a ``non-classical" probability calculus. This observation has inspired the study of more general non-classical probabilistic theories modeled on QM, the so-called generalized probabilistic theories or GPTs. However, the boundary between these putatively non-classical probabilistic theories and classical probability theory is somewhat blurry, and perhaps even conventional. This is because, as is well known, any probabilistic model can be understood in classical terms if we are willing to embrace some form of contextuality. In this talk, I want to stress that this can often be done functorially: given a category $\Cat$ of probabilistic models, there are functors $F : \Cat \rightarrow \Set_{\Delta}$ where $\Set_{\Delta}$ is the category of sets and stochastic maps. In addition to the familiar Beltrametti-Bugajski representation, I'll exhibit two others that are less well known, one involving the ``semi-classical cover" and another, slightly more special, that allows one to represent a probabilistic model with sufficiently strong symmetry properties by a model having a completely classical probabilistic structure, in which any ``non-classicality" is moved into the dynamics, in roughly the spirit of Bohmian mechanics.

(Based on http://philsci-archive.pitt.edu/16721/)

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