d=3 SIC POVMs and Elliptic Curves
APA
Hughston, L. (2007). d=3 SIC POVMs and Elliptic Curves. Perimeter Institute. https://pirsa.org/07100040
MLA
Hughston, Lane. d=3 SIC POVMs and Elliptic Curves. Perimeter Institute, Oct. 30, 2007, https://pirsa.org/07100040
BibTex
@misc{ pirsa_PIRSA:07100040, doi = {10.48660/07100040}, url = {https://pirsa.org/07100040}, author = {Hughston, Lane}, keywords = {Quantum Foundations}, language = {en}, title = {d=3 SIC POVMs and Elliptic Curves}, publisher = {Perimeter Institute}, year = {2007}, month = {oct}, note = {PIRSA:07100040 see, \url{https://pirsa.org}} }
Imperial College London
Collection
Talk Type
Subject
Abstract
The simplest algebraic curves of genus one are the nonsingular cubics in two-dimensional complex projective space. Interpreting CP^2 as the space of pure quantum states associated with a Hilbert space of dimension three, I will show how various properties of d=3 symmetric informationally complete positive operator valued measures can be understood in terms of the geometry of such curves. The resulting structure, although of considerable complexity, is very beautiful from a mathematical perspective.