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SUMMARY:Low rank as a model for quantum and classical estimation problems 
 - David Gross\, University of Freiburg
DTSTART:20141031T160000Z
DTEND:20141031T170000Z
UID:TALK55708@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:The theory of compressed sensing provides rigorous methods for
  analyzing the performance of estimators that include a sparsity-enhancing
  1-norm regularization term. Since around 2009\, a "non-commutative" versi
 on of compressed sensing has been developed. Here\, the aim is to efficien
 tly\nrecover matrices under a low-rank assumption\, most commonly using nu
 clear-norm regularization. The program was initially motivated by purely c
 lassical estimation problems - e.g. the influential "Netflix\nproblem" of 
 predicting user preferences in online shops. However\, early on\, a fruitf
 ul interaction between classical and quantum theory ensued:\nIn one direct
 ion\, it has been realized that low-rank methods lead to rigorous and very
  tight performance guarantees for quantum state estimation procedures. In 
 the other direction\, mathematical methods\noriginally developed in the co
 ntext of quantum information theory allowed for a significant generalizati
 on and simplification of the\nrigorous results on low-rank recovery. I wil
 l give an introduction to the theory\, as well as classical and quantum ap
 plications.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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