PIRSA:07100040

d=3 SIC POVMs and Elliptic Curves

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

Hughston, Lane. d=3 SIC POVMs and Elliptic Curves. Perimeter Institute, Oct. 30, 2007, https://pirsa.org/07100040 

          @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}}
          }

Lane Hughston Imperial College London

DOI 10.48660/07100040
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.