Workshop on

Quantum Mechanics: Axiomatics of Measurements and connections with Computing and Information Retrieval

Symmetry, Bias and Tomographic Efficiency

aula DOTTORATO - MERCOLEdì 28 GIUGNO, ore 14.30
  MARCUS APPLEBY, Queen Mary, University of London

"I embarked on research rather late in life, obtaining my PhD at the age of 45. Since then I have published work on the joint measurement problem, Bohmian mechanics, Contextuality, Probability, and SIC-POVMs. I earn my living as a high school teacher. I am a senior visiting fellow at Queen Mary, University of London."

Marcus Appleby

We give a Bayesian analysis of tomography, focussing on the question: for a given Bayesian prior, what is the optimal tomographic strategy? We derive two quantitative measures of tomographic efficiency, which are complementary to one another. We use these measures to discuss the relative merits of a tomographic strategy based on SIC-POVMs (symmetric, informationally complete positive operator valued measures), and one based on a full set of mutually unbiased bases (in dimensions for which such exists). We go on to analyse the tomographic efficiency of an arbitrary minimal POVM (i.e. a POVM having d2 elements, where d is the dimension of the Hilbert space). We show that for a Hilbert Schmidt uniform prior the efficiency of such a POVM can be characterized in terms of just three numbers. The methods we employ may generalize to the case of POVMs having more than d2 elements.