Quantum Information Processing and Quantum Communications

Some statistical problems of Quantum Homodyne Tomography

aula 326 - MERCOLedì 30 giugno ore 11.00
  LUIS M. ARTILES MARTINEZ, Eurandom - University of Eindohoven

Luis M. Artiles Martinez was born in June 1970. He studied Mathematics at Havana University. He did a Master class on Stochastics and Operational Research at the Mathematical Research Institute, The Netherlands, in 1997. He defended his PhD thesis in December 2001 in Utrecht University with the title "Adaptive minimax estimation in classes of smooth functions". Since then he has been working at Eurandom, the Netherlands, in the area of Quantum Statistics and in particular in a project for studying Quantum Homodyne Tomography as an inverse statistical problem.

Luis M. Artiles Martinez
  It was just recently that the problem of quantum tomography has been called to the attention of the statistical community throughout the proof of consistency results for Projection Pattern Function and Sieve Maximum Likelihood estimators of the density matrix and the Wigner function of the quantum state of light. To prove consistency means that the estimator converges to the desired state in appropriate norm. A step further in this study is to prove how fast (rate of convergence) an estimator converges as the number of samples increases. We show pointwise rates of convergence of the minimax error for the classical Kernel estimator of the Wigner function from quantum homodyne tomography data, assuming the Wigner function is in certain class.