Upcoming events

October 23, 2019 at 11:15
 
Seminar given by Markus Grassl
Title: Symmetries of Weyl-Heisenberg SIC-POVMs
 
Abstract:
SIC-POVMs are generalised quantum measurements which are of particular interest in the context of quantum state tomography and quantum key distribution. Alternatively, they can be described by d^2
normalised vectors in the d-dimensional complex vector space such that the inner product between any pair of vectors has constant modulus. It has been conjectured that SIC-POVMs exist for all dimensions and that they can be constructed as orbits of a so-called fiducial vector under the Weyl-Heisenberg group. Despite a lot of effort, exact fiducial vectors are known for only a few dimensions, and numerical ones up to around dimension 150, together with some solutions in larger dimensions. Recently, exact and numerical solutions in record-dimensions 323 and 844, respectively, have been found as part of conjectured families obeying additional symmetries.
The talk will present the symmetries for this putative family together with generalisations. Links to number-theoretic conjectures in this context will be presented as well. This allows to convert numerical solutions of moderate precision into exact solutions, including dimension 844 mentioned above as well as the new record dimension 1299.
 
Place: International Centre for Theory of Quantum Technologies, Wita Stwosza 63, Gdansk (Chemistry Department), third floor, seminar room no. F305
 

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