ELFT HÍRADÓ

[Király Beáta <kiraly.beata AT atomki.hu>]

Improved local models and new Bell inequalities via Frank-Wolfe algorithms 

Előadó: Dr. Sébastien Designolle (Zuse-Institut Berlin - ZIB, Berlin, 
Germany) 



Időpont: 2023-02-28 kedd 11:00 

Helyszín: Atomki, tanácsterem (Debrecen, Bem tér 18/c, I. épület alagsora) 








Abstract: 





In Bell scenarios with two outcomes per party, we algorithmically consider 
the two sides of the membership problem for the local polytope [1]: 
constructing local models and deriving separating hyperplanes, that is, Bell 
inequalities. We take advantage of the recent developments in so-called 
Frank--Wolfe algorithms to significantly increase the convergence rate of 
existing methods. As an application, we study the threshold value for the 
nonlocality of two-qubit Werner states under projective measurements. Here, 
we improve on both the upper and lower bounds present in the literature, 
almost halving the length of the accompanying range. Importantly, our bounds 
are entirely analytical and yield refined bounds 1.4376≤K_G(3)≤1.4546 on the 
value of the Grothendieck constant of order three. We also demonstrate the 
efficiency of our approach in multipartite Bell scenarios, and present the 
first local models for all projective measurements with visibilities 
noticeably higher than the entanglement threshold. We make our entire code 
accessible as a Julia library called BellPolytopes.jl. 




[1] S. Designolle, G. Iommazzo, M. Besançon, S. Knebel, P. Gelß, and S. 
Pokutta, https://arxiv.org/abs/2302.04721 (2023). 











--- 
Király Beáta, PhD 
Atomki / Atommagkutató Intézet 
C: 4026 Debrecen, Bem tér 18/c 
T: +36 52 509 200 
E: kiraly.beata AT atomki.hu 
W: [ http://www.atomki.hu/ | www.atomki.hu ]