Workshop on QUANTUM MEASUREMENTS AND OPERATIONS FOR CRIPTOGRAPHY AND INFORMATION PROCESSING
Quantum Measurements and Operations for Criptography and Information Processing
Reconciliation of Bayes and frequentist approaches to state estimation
aula DOTTORATO - MERCOLedì 2 MARZO ore 14.00>VITAE:
Richard Gill (born 1951) is Professor in Mathematical Statistics at the
University of Utrecht, Netherlands. He is a member of the Dutch Academy
of Sciences. In recent years he has been working on the statistical approach
to quantum state reconstruction problems, and on statistical aspects of
Bell-type experiments.
Two competing approaches exist in the literature:
1) the Bayesian approach whereby we exactly optimize, for fixed N, the average fidelity: we can sometimes find an exactly optimal solution but it typically depends on a felicitious and specific choice of prior distribution and loss function (fidelity)
2) the frequentist large sample approach where we approximately optimize, for large N, the average value of a quadratic approximation to the loss function with respect to an asymptotic distribution of the error in the reconstruction, for given fixed (though of course unknown, and arbitrary) quantum state; no prior distribution is assumed at all.
I'll discuss relations between solutions of the two problems, advantages and disadvantages, with examples (recent joint work with the Barcelona group).
