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PIRSA:07100040

Video URL

https://pirsa.org/07100040

d=3 SIC POVMs and Elliptic Curves

Hughston, L. (2007). d=3 SIC POVMs and Elliptic Curves. Perimeter Institute for Theoretical Physics. https://pirsa.org/07100040

Lane Hughston Imperial College London

Talk numberPIRSA:07100040
DOI10.48660/07100040
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
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.