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SUMMARY:Spectral thresholding in quantum state estimation for low rank sta
 tes - Madalin Guta\, University of Nottingham
DTSTART:20150220T160000Z
DTEND:20150220T170000Z
UID:TALK56944@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Quantum Information and Technology is a young research area at
  the overlap between quantum physics and "classical" fields such as comput
 ation theory\, information theory\, statistics and probability and control
  theory. The paradigm is that quantum systems such as atoms and photons\, 
 are carriers of a new type of information\, whose processing is governed b
 y the formalism of quantum mechanics. This has found numerous applications
  in computation\, cryptography\, precision metrology\, and significant exp
 erimental efforts are dedicated towards the practical implementation of su
 ch technologies. \n\nOne of the key component of many quantum engineering 
 experiments is the statistical analysis of measurement data. In particular
 \, in ion trap experiments one deals with the problem of reconstructing la
 rge density matrices (positive\, complex matrices of trace one) representi
 ng the joint state of several atoms\, from i.i.d. counts of collected from
  measurements on identical prepared atoms. Since the matrix dimension scal
 es exponentially with the number of atoms\, current techniques can cope wi
 th at most 10 atoms\, and one of the key questions is how statistically re
 construct large dimensional states.\n\n\nIn this talk I will discuss two n
 ew estimation methods for quantum tomography in ion experiments\, their th
 eoretical properties and simulations results. Both methods consist in comp
 uting the least squares estimator as first step\, followed by setting cert
 ain "statistically insignificant" eigenvalues to zero. Since in many exper
 iments the goal is to produce a pure (rank one) density matrix\, \nlow ran
 k density matrices provide a natural lower dimensional model for experimen
 ts. For such states\, the thresholding methods provide a significant impro
 vement compared with the least squares estimator\; in fact\, our upper and
  lowe bounds show that up to logarithmic factors\, the mean square error h
 as the optimal scaling in terms of dimension and sample size. \n
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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