Workshop on QUANTUM INFORMATION PROCESSING AND QUANTUM COMMUNICATIONS

Quantum Information Processing and Quantum Communications
Quantum state estimation and large deviations

aula DOTTORATO Mercoledì 28 aprile ore 11.00 

MICHAEL
KEYL, University of Braunschweig and QUIT at Pavia 
>VITAE:
Michael Keyl obtained his PhD in 1994 from the TU Berlin, where he worked
on quantum field theory on curved spacetimes.
He started to work on quantum information theory in 1997 at the Institut
of Mathematical Physics of the TU Braunschweig, where he is currently
a faculty member (Privatdozent).
His main fields of interest include mathematical and conceptual foundations
of quantum theory, in particular of quantum information theory.


Abstract 


Quantum state estimation and large deviations
In this talk we investigate the large deviation behaviour of estimation
schemes for arbitrary mixed states of finite dimensional quantum systems.
In this context we present two main results:
Using relations to quantum hypothesis testing, we show that the rate function
is always bounded from above by the quantum relative entropy. In addition
we consider an explicit scheme which is based on covariant observables and
representation theory of unitary groups, and which extends previous results
concerning the estimation of the spectrum of the density operator. The corresponding
rate function, however, is smaller than the relative entropy, and this leads
to the question whether the proposed scheme can be further improved. 

