Karvonen, Martti;
(2019)
Categories of Empirical Models.
In:
Electronic Proceedings in Theoretical Computer Science (EPTCS).
(pp. pp. 239-252).
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Abstract
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between measurement scenarios, and allowing for stochastic mappings of outcomes to outcomes. This formalizes an intuitive idea of using one empirical model to simulate another one with the help of pre-shared classical randomness. This allows one to reinterpret concepts and earlier results in terms of morphisms. Most notably: non-contextual models are precisely those allowing a morphism from the terminal object; contextual fraction is functorial; Graham-reductions induce morphisms, reinterpreting Vorob’evs theorem; contextual models cannot be cloned.
| Type: | Proceedings paper |
|---|---|
| Title: | Categories of Empirical Models |
| Event: | 15th International Conference on Quantum Physics and Logic (QPL) co-located with 34th Conference on the Mathematical Foundations of Programming Semantics (MFPS) |
| Location: | Dalhousie Univ, Halifax, CANADA |
| Dates: | 3 Jun 2018 - 7 Jun 2018 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4204/eptcs.287.14 |
| Publisher version: | https://doi.org/10.4204/EPTCS.287.14 |
| Language: | English |
| Additional information: | © M. Karvonen This work is licensed under the Creative Commons Attribution License. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10193412 |
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