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SUMMARY:A conic approach to entangled-assisted graph parameters - Piovesan
 \, T (Centrum voor Wiskunde en Informatica (CWI))
DTSTART:20130719T103000Z
DTEND:20130719T110000Z
UID:TALK46299@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Graph parameters as the independence and the chromatic number 
 are related to classical (zero-error) communication problems. It is known 
 that allowing the presence of entanglement\, one of quantum mechanics most
  peculiar feature\, might increase the efficiency of the (zero-error) comm
 unication. However there are still many open problem\, for example the max
 imal possible separation between classical and quantum communication\, com
 putational complexity and approximation of the quantum variant of the grap
 h parameters etc. We propose a new framework for studying the quantum para
 meters\, introducing a cone that lies between the completely positive and 
 the double non-negative one. We say that a matrix X is in this cone if the
 re exists a set of positive semidefinite matrices {A_i} such that the i\,j
 -th entry of X is equal to the inner product between A_i and A_j. Testing 
 membership of the dual cone is equivalent to determine whether a particula
 r polynomial is trace positive over all the real symmetric matrices of any
  dimension. This problem is therefore related to a special case of the Con
 nes embedding conjecture. This conic approach allow us to prove better bou
 nds for the quantum variant of the graph parameters\, to have a more unifi
 ed framework and hopefully to build approximation hierarchies.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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