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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://cms.ku.dkObvius::Document=HASH(0x7fb4dec269d8)
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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