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|
|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).