Reexamination of optimal quantum state estimation of pure states
Abstract
A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by M. Hayashi in terms of an infinite set of covariant positive operator valued measures (POVM's) and by Bruss and Macchiavello establishing a connection to optimal quantum cloning. An explicit condition for POVM measurement operators for optimal estimators is obtained, by which we construct optimal estimators with finite POVM using exact quadratures on a hypersphere. These finite optimal estimators are not generally universal, where universality means the fidelity is independent of input states. However, any optimal estimator with finite POVM for M(>N) copies is universal if it is used for N copies as input.
Cite
@article{arxiv.quant-ph/0410207,
title = {Reexamination of optimal quantum state estimation of pure states},
author = {A. Hayashi and T. Hashimoto and M. Horibe},
journal= {arXiv preprint arXiv:quant-ph/0410207},
year = {2009}
}
Comments
v3(journal version): title changed, presentation improved