>VITAE:
Rafal DemkowiczDobrzanski did his master thesis (“Cloning of quantum
states”) in 2003 at the faculty of physics, Warsaw University, under
supervision of Krzysztof Wodkiewicz.
Presently he is doing a PhD at the Center for theoretical physics, Warsaw,
under supervision of Marek Kus. Main areas of interests: quantum cloning,
state estimation, multipartite entanglement and entanglement production
in chaotic systems. 


State estimation is usually analyzed in the situation
when copies are in a product state, either mixed or pure. I will present
the concept of state estimation on correlated copies. Using a correlated
state one tries to estimate as good as possible the direction of the Bloch
vector of a single particle reduced density matrix. I will present the
optimal fidelity of such estimation for all permutation invariant states
and show the optimal state, which yields the highest estimation fidelity
among the states with the same reduced density matrix.
Interestingly this state is not a product state.
It will be also pointed out that states produced by optimal universal
cloning machines are the worst from the point of view of estimating the
reduced density matrix.
