Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
Speaker: | Levent Tunçel |
---|---|
Affiliation: | University of Waterloo |
Room: | Mathematics & Computer Building (MC) 5158 |
The problem of proving (or disproving) the existence of symmetric informationally complete positive operator valued measures (SICs) has been the focus of much effort in the quantum information community during the last 12 years. In this talk we describe the Galois invariances of Weyl-Heisenberg covariant SICs (the class which has been most intensively studied). It is a striking fact that the published exact solutions (in dimensions 2~V16, 19, 24, 35 and 48) are all expressible in terms of radicals, implying that the associated Galois groups must be solvable. Building on the work of Scott and Grassl (J. Math. Phys. 51 042203 (2010)) we investigate the Galois group in more detail. We show that there is an intriguing interplay between the Galois and Clifford group symmetries. We also show that there are a number of interesting regularities in the Galois group structure for the cases we have examined. We conclude with some speculations about the bearing this may have on the SIC existence problem.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.