Quantum estimation of unknown parameters

TL;DR

This paper explores optimal quantum measurement strategies for parameter estimation, proposing a modified inequality to determine measurement optimality and an adaptive approach for unknown parameters.

Contribution

It introduces a modified quantum Van Trees inequality to assess measurement optimality and proposes an adaptive estimation strategy for unknown parameters.

Findings

Modified quantum Van Trees inequality for measurement optimality

Adaptive estimation strategy based on the inequality

Framework for estimating unknown quantum system parameters

Abstract

We discuss the problem of finding the best measurement strategy for estimating the value of a quantum system parameter. In general the optimum quantum measurement, in the sense that it maximizes the quantum Fisher information and hence allows one to minimize the estimation error, can only be determined if the value of the parameter is already known. A modification of the quantum Van Trees inequality, which gives a lower bound on the error in the estimation of a random parameter, is proposed. The suggested inequality allows us to assert if a particular quantum measurement, together with an appropriate estimator, is optimal. An adaptive strategy to estimate the value of a parameter, based on our modified inequality, is proposed.