Berlin 2014 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
Q: Fachverband Quantenoptik und Photonik
Q 58: Quantum information: Concepts and methods IV
Q 58.3: Vortrag
Freitag, 21. März 2014, 11:00–11:15, Kinosaal
A Partial Derandomization of PhaseLift using Spherical Designs — David Gross1, Felix Krahmer2, and •Richard Kueng1 — 1Physikalisches Institut, Universität Freiburg, Deutschland — 2Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Deutschland
The problem of retrieving phase information from amplitudes alone (equivalently: recovering a signal from quadratic measurements) has appeared in many scientific disciplines over the last century.
PhaseLift is a recently introduced algorithm for that task which is computationally efficient, numerically stable, and comes with rigorous performance guarantees. PhaseLift is optimal in the sense that the number of amplitude measurements required for phase reconstruction scales linearly with the dimension of the signal. However, it specifically demands Haar-random measurement vectors — a limitation that restricts practical utility and obscures the specific properties of measurement ensembles that enable phase retrieval.
Here we present a partial derandomization of PhaseLift that only requires sampling from t-designs. Such configurations have been studied extensively in quantum information and are known to serve as a general-purpose tool for de-randomization. Following this philosophy, we prove reconstruction guarantees for a number of measurements that depends on the degree t of the design.
This work is another instance of a fruitful application of quantum information ideas to the mathematical study of data analysis problems.