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CATEGORIES:CQIF Seminar
SUMMARY:Convex separation from convex optimization for lar
ge-scale problems - Steve Brierley\, University of
Cambridge
DTSTART;TZID=Europe/London:20161110T141500
DTEND;TZID=Europe/London:20161110T151500
UID:TALK68782AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68782
DESCRIPTION:I'll present a new scheme to prove separation betw
een a point and an arbitrary convex set S via call
s to an oracle able to perform linear optimization
s over S. Compared to other methods\, it has almos
t negligible memory requirements and the number of
calls to the optimization oracle does not depend
on the dimensionality of the underlying space. We
study the speed of convergence of the scheme under
different promises on the shape of the set S and/
or the location of the point\, validating the accu
racy of the theoretical bounds with numerical exam
ples. \n\nI will then present some applications of
the scheme in quantum information theory. The alg
orithm out-performs existing linear programming me
thods for certain large scale problems\, allowing
us to certify nonlocality in bipartite scenarios w
ith upto 42 measurement settings. I'll show how to
use the algorithm to upper bound the visibility o
f two-qubit Werner states\, hence improving known
lower bounds on Grothendieck's constant KG(3). Sim
ilarly\, we compute new upper bounds on the visibi
lity of GHZ states and on the steerability limit o
f Werner states for a fixed number of measurement
settings.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Steve Brierley
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