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 

RICHARD
GILL, Utrecht University 
>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
Belltype experiments.


Abstract 


I consider problems of state estimation in the case of N
identical copies of an unknown state on a finite dimensional Hilbert space.
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). 

