PIRSA:11010113

From groups to non-locality via categories

Edwards, W. (2011). From groups to non-locality via categories. Perimeter Institute. https://pirsa.org/11010113

Edwards, William. From groups to non-locality via categories. Perimeter Institute, Jan. 25, 2011, https://pirsa.org/11010113 

          @misc{ pirsa_PIRSA:11010113,
            doi = {10.48660/11010113},
            url = {https://pirsa.org/11010113},
            author = {Edwards, William},
            keywords = {Quantum Foundations},
            language = {en},
            title = {From groups to non-locality via categories},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {jan},
            note = {PIRSA:11010113 see, \url{https://pirsa.org}}
          }

William Edwards

Talk number
PIRSA:11010113
Collection
Talk Type
Subject
Abstract
Symmetric monoidal categories provide a convenient and enlightening framework within which to compare and contrast physical theories on a common mathematical footing. In this talk we consider two theories: stabiliser qubit quantum mechanics and the toy bit theory proposed by Rob Spekkens. Expressed in the categorical framework the two theories look very similar mathematically, reflecting their common physical features. There are differences though: in particular a finite Abelian group emerges naturally in the categorical framework, and this group is different in each case ($Z_4$ for the stabiliser theory and $Z_2 \times Z_2$ for the toy bit theory). It turns out that this mathematical difference corresponds directly with a key physical difference between the theories: the stabiliser theory cannot be modelled by local hidden variables, while the toy bit theory can. This analysis can be extended to other Abelian groups yielding a group-theoretic criterion for determining the possibility of local hidden variable interpretations for other physical theories.