PIRSA:07100040 Scientific Series Quantum Foundations

DOI10.48660/07100040

Series: Quantum Foundations

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}}
}

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.

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