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Thomas Durt (Institut Fresnel, Ecole Centrale Marseille, France)
June 3, 2021 @ 13:00 - 14:00
Title: Applications of the Heisenberg-Weyl group to quantum state tomography with focus on dimensions 2 (quits) and 3 (qutrits)
Quantum state tomography aims at estimating an a priori unknown quantum state with maximal efficiency.
The Heisenberg-Weyl group is obtained by composing phase-space displacements in position (translations) and momentum (boosts); it is a representation of the Galilei group.
Heisenberg-Weyl displacement operators are intimately associated to the Wigner operators which are quantum localisation operators in phase-space.
Mutually Unbiased Bases (MUBs) and Symmetric Informationally Complete POVMs (SICs) play a central role in relation with the tomographic applications associated to the aforementioned operators.
Our goal is to define these objects, to describe the elegant symmetries and geometric structures associated to them, and to emphasize their relevance in the framework of quantum state tomography.
Link to the seminar here
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