Speaker: Palle Jorgensen (University of Iowa).

Title: "Some connection between operator algebras and quantum information theory".


In the talk, we will recall some connections between the theory of C*-algebras and mathematical physics, with special emphasis on quantum information theory.

The focus will be on C*-algebras, or rather classes of C*-algebras; the Cuntz algebras, and the deformation C*-algebras, such as the rotation algebras, and the q-deformation algebras derived from the Fermion/Boson algebras. We will stress the following key issues on C*-algebras: their isomorphism classes, their representations, and some theorems on stability of C*-isomorphism classes. The deformation C*-algebras are relevant for particle physics, for example for quons and the Gibbs paradox.

Representations of the Cuntz algebras, or the Cuntz relations, play a key role in analysis/synthesis filters in signal processing, both for transmission of speech and of images. They are used in compression in wavelet algorithms, and, at the same time, in a different guise, in quantum programs from quantum computation. While the famous factoring algorithm of P. Shor, and the search algorithm of L. Grover, are the two known quantum algorithms which are closest to being "practical", and at the same time in showing dramatic speedup compared to the corresponding classical algorithms, there are others, and the wavelet algorithm is one.

In the talk we will compare the wavelet algorithms in the two cases, classical and quantum. The role played by quantum error-correction codes will be touched on.

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