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February 28, 2019
Sporadic SICs and Exceptional Lie Algebras II
Posted by John Baez
guest post by Blake C. Stacey
Today, we carry forward with the project we began last week: exploring Symmetric Informationally Complete quantum measurements, otherwise known as SICs. They’re really just maximal sets of equiangular lines in a complex vector space!
In our first post, we laid the groundwork and studied one example: a set of four equiangular lines in . Now, we move up a dimension and investigate a set of 9 equiangular lines in . This will bring the exceptional Lie algebras into the narrative, and we’ll also get a chance to greet a biodiversity measure and a polytope known as the 24-cell.
February 20, 2019
Tychonoffication
Posted by John Baez
Joshua Meyers is a grad student in my real analysis class. We had an interesting conversation about topology and came up with some conjectures. Maybe someone has already proved them. I just want to write them down somewhere.
Sporadic SICs and Exceptional Lie Algebras I
Posted by John Baez
guest post by Blake C. Stacey
Sometimes, mathematical oddities crowd in upon one another, and the exceptions to one classification scheme reveal themselves as fellow-travelers with the exceptions to a quite different taxonomy. I am grateful to John for giving me the opportunity to discuss one such confluence, where quantum information theory comes together with geometry, root systems and even the octonions.
In what follows, I will be divvying up these notes into blog posts. The first step is to introduce the geometrical statement of the SIC problem. Then, we’ll establish some basics about quantum theory, which may be fairly standard if you learned out of Mike and Ike while being a little un-standard outside of quantum information.
February 7, 2019
Applied Category Theory 2019
Posted by John Baez
I hope to see you at this conference!
- Applied Category Theory 2019, July 15-19, 2019, Oxford, UK.
Here’s some information about it, such as how to submit papers.
February 4, 2019
Jacobi Manifolds
Posted by John Baez
Here at the conference Foundations of Geometric Structures of Information 2019, Aïssa Wade of Penn State gave a talk about Jacobi manifolds. She got my attention with these words: “Poisson geometry is a good framework for classical mechanics, while contact geometry is the right framework for classical thermodynamics. Jacobi manifolds are a natural bridge between these.”
So what’s a Jacobi manifold?