Asymptotic estimation of shift parameter of a quantum state
Abstract
We develop an asymptotic theory of estimation of a shift parameter in a pure quantum state to study the relation between entangled and unentangled covariant estimates in the analytically most transparent way. After recollecting basics of estimation of shift parameter in Sec. 2, we study the structure of the optimal covariant estimate in Sec. 3, showing how entanglement comes into play for several independent trials. In Secs. 4,5 we give the asymptotics of the performance of the optimal covariant estimate comparing it with the ``semiclassical'' unentangled covariant estimation in the regular case of finite variance of the generator of the shift group. Sec. 6 is devoted to covariant estimation in the case where the regularity assumption is violated.
Cite
@article{arxiv.quant-ph/0307225,
title = {Asymptotic estimation of shift parameter of a quantum state},
author = {A. S. Holevo},
journal= {arXiv preprint arXiv:quant-ph/0307225},
year = {2011}
}
Comments
18 pages. Comments and new references are added following discussions at the Workshop "Quantum Measurement and Quantum Stochastics" at Maphysto, University of Aarhus, August 7-12, 2003, where the initial version of the paper was presented