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DESCRIPTION:Speaker: John Wright
\nAbstract:
\nAn experiment produces an u
 nknown mixed state\, and you would like to learn some property of this sta
 te.  How do you do this?  The standard approach is to rerun the experime
 nt multiple times and perform some measurement on the copies produced.  T
 he goal is then to learn or test the property using the smallest number of
  copies possible.  In some cases\, such as performing tomography on rank 
 one pure states\, researchers have designed algorithms which are optimal i
 n their copy complexity.  However\, for many basic properties\, including
  things as basic as estimating a mixed state's spectrum\, this remains an 
 open problem.
\n
\nIn this talk\, we consider learning and testing propert
 ies which depend only on the mixed state's spectrum.  Natural problems in
  this space include learning its spectrum\, estimating its von Neumann ent
 ropy\, or testing whether it is low rank.  Our results include (i) a new 
 upper bound for learning a mixed state's spectrum and (ii) an optimal algo
 rithm for testing whether a mixed state is equal to the maximally mixed st
 ate.  We use techniques from the asymptotic theory of the symmetric group
 \; in particular\, we rely on Kerov's algebra of observables to help us st
 udy the moments of random Young diagrams.
\n \nJoint work with Ryan O'Donn
 ell.\n\nhttps://qmath.ku.dk/events/quantum-lunch/quantum-lunch-2015/23-15/
 
SUMMARY:Quantum Lunch: Learning and testing of mixed state spectra
LOCATION:The Quantum Lunch room\, 04.4.20
ORGANIZER:Christian Majenz
DTSTART:20150603T100000Z
DTSTAMP:20150603T100000Z
DTEND:20150603T110000Z
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