[Alta-Logic] Peripatetic Seminar tomorrow!

[Robin Cockett]

Speaker: Clifton Cunningham
Title: Some observations on the Hilbert spaces of quantum information
Place: ICT 618
Time: 12:30pm Wed, Sept 15th

Abstract: The finite-dimensional Hilbert spaces that appear in quantum
information, equipped with the quantum Fourier transform, appear in
number theory (specifically, the study of automorphic representations)
as finite-dimensional subspaces of an infinite-dimensional Hilbert
space, also equipped with a Fourier transform. This ambient Hilbert
space consists of complex-valued square-integrable (generalized)
functions on a natural locally-compact topological space and the
Fourier transform it carries is given by an integral over this
topological space. Moreover, when we restrict this `continuous'
Fourier transform to the Hilbert spaces of quantum information, we
recover the `discrete' quantum Fourier transform. In this talk we
explain how to interpret states in quantum information as continuous
functions on a locally-compact topological space. Joint work with Adrian 
Keet.