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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A conic approach to entangled-assisted graph param
eters - Piovesan\, T (Centrum voor Wiskunde en Inf
ormatica (CWI))
DTSTART;TZID=Europe/London:20130719T113000
DTEND;TZID=Europe/London:20130719T120000
UID:TALK46299AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/46299
DESCRIPTION:Graph parameters as the independence and the chrom
atic number are related to classical (zero-error)
communication problems. It is known that allowing
the presence of entanglement\, one of quantum mech
anics most peculiar feature\, might increase the e
fficiency of the (zero-error) communication. Howev
er there are still many open problem\, for example
the maximal possible separation between classical
and quantum communication\, computational complex
ity and approximation of the quantum variant of th
e graph parameters etc. We propose a new framework
for studying the quantum parameters\, introducing
a cone that lies between the completely positive
and the double non-negative one. We say that a mat
rix X is in this cone if there exists a set of pos
itive semidefinite matrices {A_i} such that the i\
,j-th entry of X is equal to the inner product bet
ween A_i and A_j. Testing membership of the dual c
one is equivalent to determine whether a particula
r polynomial is trace positive over all the real s
ymmetric matrices of any dimension. This problem i
s therefore related to a special case of the Conne
s embedding conjecture. This conic approach allow
us to prove better bounds for the quantum variant
of the graph parameters\, to have a more unified f
ramework and hopefully to build approximation hier
archies.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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