[DMO] Bram Bekker: Semidefinite programming bounds for distance-avoiding set problems in quantum communication

23 juni 2023 14:00 t/m 15:00 - Locatie: EEMCS 01.230 Elektron | Zet in mijn agenda

Witsenhausen’s problem asks for the set with largest area on the n-dimensional unit sphere such that no two points in this set are orthogonal. A very simple argument shows that this area relates to a lower bound on the efficiency of quantum communication channels, as shown by A. Montina. By exposing Witsenhausen’s problem as a maximal independent set problem on an infinite graph, we can use semidefinite programming to obtain upper bounds to this maximal area. Using copositive cuts, we developed a hierarchy of strengthenings of the Lovász theta-number to obtain the best upper bounds known. A result of theoretical significance is the proof that this copositive hierarchy converges to exactly the independence number of the graph.