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CATEGORIES:Statistics
SUMMARY:Spectral thresholding in quantum state estimation
for low rank states - Madalin Guta\, University of
Nottingham
DTSTART;TZID=Europe/London:20150220T160000
DTEND;TZID=Europe/London:20150220T170000
UID:TALK56944AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/56944
DESCRIPTION:Quantum Information and Technology is a young rese
arch area at the overlap between quantum physics a
nd "classical" fields such as computation theory\,
information theory\, statistics and probability a
nd control theory. The paradigm is that quantum sy
stems such as atoms and photons\, are carriers of
a new type of information\, whose processing is go
verned by the formalism of quantum mechanics. This
has found numerous applications in computation\,
cryptography\, precision metrology\, and significa
nt experimental efforts are dedicated towards the
practical implementation of such technologies. \n\
nOne of the key component of many quantum engineer
ing experiments is the statistical analysis of mea
surement data. In particular\, in ion trap experim
ents one deals with the problem of reconstructing
large density matrices (positive\, complex matrice
s of trace one) representing the joint state of se
veral atoms\, from i.i.d. counts of collected from
measurements on identical prepared atoms. Since t
he matrix dimension scales exponentially with the
number of atoms\, current techniques can cope with
at most 10 atoms\, and one of the key questions i
s how statistically reconstruct large dimensional
states.\n\n\nIn this talk I will discuss two new e
stimation methods for quantum tomography in ion ex
periments\, their theoretical properties and simul
ations results. Both methods consist in computing
the least squares estimator as first step\, follow
ed by setting certain "statistically insignificant
" eigenvalues to zero. Since in many experiments t
he goal is to produce a pure (rank one) density ma
trix\, \nlow rank density matrices provide a natur
al lower dimensional model for experiments. For su
ch states\, the thresholding methods provide a sig
nificant improvement compared with the least squar
es estimator\; in fact\, our upper and lowe bounds
show that up to logarithmic factors\, the mean sq
uare error has the optimal scaling in terms of dim
ension and sample size. \n
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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