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).

A note on Fisher-Helstrom information inequality in pure state models

LUATI, ALESSANDRA
2008

Abstract

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).
A. Luati
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/64633
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