Estimation of gradients in quantum metrology

Sanah Altenburg, Michał Oszmaniec, Sabine Wölk, Otfried Gühne

Published 2017-03-27Version 1

We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Classically, gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the ions and therefore suffers from collective dephasing, so we concentrate on states which are insensitive to these fluctuations. States from the decoherence-free subspace (DFS) allow to measure the gradient directly, without estimating the magnetic field. We use the framework of quantum metrology to assess the maximal accuracy of the precision of gradient estimation. We find that states from the DFS achieve the highest measurement sensitivity, as quantified by the quantum Fisher information and find measurements saturating the quantum Cram\'er-Rao bound.