Title: Generalising the Coecke-Pavlovic-Vicary Correspondence
Abstract:
In their paper [1], Coecke-Palvovic-Vicary (CPV) gives a correspondence between orthogonal bases in finite-dimensional Hilbert Spaces (FdHilb) and Commutative-Dagger Frobenius algebras in FdHilb. In the first part of my talk, I will go over this correspondence and the associated categorical statements.
In the second part of my talk, I will give an outline of the programme about how this correspondence can be generalised to arbitrary dimensions. I will first introduce the ingredients involved- Finiteness spaces, Lefschetz Spaces and time-permitting linear monoids and then will give a few results connecting these mathematical objects.
Reference:
[1] Coecke, B., Pavlovic, D., & Vicary, J. (2012). A new description of orthogonal bases. Mathematical Structures in Computer Science, 23(3).
