State estimation on correlated copies
Rafał Demkowicz-Dobrzański · Physical Review A · 2005
State estimation is usually analyzed in the situation when copies are in a product state, either mixed or pure. We investigate here the concept of state estimation on correlated copies. We analyze state estimation on correlated $N$-qubit states, which are permutationally invariant. Using a correlated state we try to estimate as good as possible the direction of the Bloch vector of a single-particle reduced density matrix. We derive the optimal fidelity for all permutation invariant states. We find 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. We also point out that states produced by optimal universal cloning machines are the worst, from the point of view of estimating the reduced density matrix.