Title: A Note on Fisher-Helstrom Information Inequality in Pure State Models

Author(s): Alessandra Luati
Issue: Volume 70 Series A Part 1 Year 2008
Pages: 25 -- 37
This paper concerns the design problem of choosing the measurement that provides the maximum Fisher information for the unknown parameter of a quantum system. We show that when the system under investigation is described by a one-parameter $n$-dimensional pure state model an optimal measurement exists, such that Fisher information attains the upper bound constituted by Helstrom information. A characterisation theorem and two strategies of implementations are derived and discussed. These results generalise to $n$-dimensional spaces those obtained for $n = 2$ by Barndorff-Nielsen and Gill (2000).
AMS (2000) subject classification. Primary 62B05; secondary 62F10.
Keywords and phrases: Classical and quantum information, Cramer-Rao type bounds, attaining measurements, rank-one matrices, spin systems.