DPG Phi
Verhandlungen
Verhandlungen
DPG

Berlin 2024 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

QI: Fachverband Quanteninformation

QI 1: Quantum Foundations

QI 1.9: Vortrag

Montag, 18. März 2024, 12:00–12:15, HFT-FT 101

Attempting to Simplify the Search for SIC-POVMs — •Ghislaine Coulter-de Wit1, 2, David Llamas1, Matt Weiss1, and Christopher Fuchs11University of Massachusettes Boston, Boston, USA — 2Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Deutschland

Symmetric informationally complete quantum measurements or SIC-POVMs are interesting from a number of perspectives. For example in QBism, SIC-POVMs give a way of representing the Born Rule such that the form minimizes the distinction between it and the classical law of total probability [DeBrota, Fuchs, and Stacey, Phys. Rev. Res. 2, 013074 (2020)]. However, it is unclear whether they exist in all dimensions. In the search for SIC-POVMs, we are most interested in the group covariant case, where the problem boils down to finding a single fiducial vector for generating the whole structure. For finite dimensions d, this amounts to finding a solution to d2 simultaneous fourth-order polynomial equations generated by the discrete Weyl-Heisenberg group. However, it has been conjectured that it is already enough to satisfy only 3d/2 of the defining equations to find a solution [Appleby, Dang, and Fuchs, Entropy 16, 1484 (2014)]. Using techniques of gradient descent we find strong correlations in the solutions between the conjecture and full d2 equations. These numerical results imply that the conjecture is true, dropping the complexity of numerically searching for SICs from a quadratic to a linear number of equations in d.

Keywords: QBism; SIC-POVM; Computational results; Weyl-Heisenberg group

100% | Mobil-Ansicht | English Version | Kontakt/Impressum/Datenschutz
DPG-Physik > DPG-Verhandlungen > 2024 > Berlin