
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 
>PRESENTATION:
"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 SICPOVMs.
I earn my living as a high school teacher. I am a senior visiting fellow
at Queen Mary, University of London." 

Abstract 


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 SICPOVMs (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.


