Noisy Metrology: A saturable lower bound on quantum Fisher information

TL;DR

This paper introduces a practical, saturable upper bound on quantum Fisher information for parameter estimation, applicable to open quantum systems, improving the accuracy of quantum metrology predictions.

Contribution

It presents a new, easily computable upper bound on quantum Fisher information that is saturable and applicable to both semigroup and non-semigroup open quantum dynamics.

Findings

The bound is straightforward to compute from quantum maps.

It applies to a wide class of open quantum systems.

Demonstrated effectiveness through three main examples.

Abstract

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision of estimation is introduced. Unlike the bounds previously introduced in the literature, the upper bound is saturable and yields a practical instruction to estimate the parameter through preparing the optimal initial state and optimal measurement. The bound is based on the underling dynamics and its calculation is straightforward and requires only the matrix representation of the quantum maps responsible for encoding the parameter. This allows us to apply the bound to open quantum systems whose dynamics are described by either semigroup or non-semigroup maps. Reliability and efficiency of the method to predict the ultimate precision limit are demonstrated by {three} main examples.