Abstract
Given identical copies of the state of a quantum two-level system, we analyze its optimal estimation. We consider two situations: general pure states and (pure) states restricted to lie on the equator of the Bloch sphere. We perform a complete and comprehensive analysis of the optimal schemes based on local measurements, and give results (optimal measurements, maximum fidelity, etc.) for arbitrary , not necessarily large, within the Bayesian framework. We also make a comparative analysis of the asymptotic limit of these results with those derived from a (pointwise) Cramér-Rao type of approach. We give explicit schemes based on local measurements and no classical communication that saturate the fidelity bounds of the most general collective schemes.
- Received 22 December 2004
DOI:https://doi.org/10.1103/PhysRevA.71.062318
©2005 American Physical Society