# Enhancing sensitivity in quantum metrology by Hamiltonian extensions

## TL;DR

This paper demonstrates that for general Hamiltonians in quantum metrology, it is possible to enhance sensitivity and reach optimal bounds without ancillas by modifying the Hamiltonian itself, with applications in NV-center magnetometry.

## Contribution

It introduces methods to increase quantum Fisher information by Hamiltonian extensions without using ancillas, broadening quantum metrology capabilities.

## Key findings

- Hamiltonian extensions can improve quantum Fisher information.
- Enhancement methods do not require ancillas.
- Applications demonstrated in NV-center magnetometry.

## Abstract

A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it \emph{is} possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term to the original Hamiltonian. Both methods do not make use of any ancillas and show therefore that for quantum channel estimation with arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with NV-center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe.