Workshop on QUANTUM MEASUREMENTS AND OPERATIONS FOR CRIPTOGRAPHY AND INFORMATION PROCESSING

Quantum Measurements and Operations for Criptography
and Information Processing
Asymptotic lower bounds to global Bayes risk in state
estimation

aula dottorato  Martedì 10 Maggio, ore 16.00 

RICHARD
GILL, Utrecht University 
>VITAE:
Richard Gill 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 became involved in Quantum Mechanics, and has been
working on the statistical approach to quantum state reconstruction problems,
and on statistical aspects of Belltype experiments. 

Abstract 


Suppose we are given N copies of a state rho depending
on a vector of unknown parameters theta. Suppose we also have a prior
distribution for theta and a smooth loss function (e.g., 1fidelity),
and we want to choose a (collective) measurement and accompanying dataprocessing
(an estimator) in order to minimize the expected loss. I conjecture that
under mild conditions on the prior and on the family of states, the following
is a sharp asymptotic lower bound to N times the risk: the average with
respect to the prior distribution of the Holevo quantum CramerRao bound
C computed for the local quadratic approximation to the loss function.
I will prove the result in some important special cases using the van
Trees inequality, and show how the result would be true under a very plausible
relative compactness conjecture concerning sequences of quantum measurements
on product systems, which seems worth investigating.


