# Hannover 2013 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# A: Fachverband Atomphysik

## A 3: Precision measurements and metrology I (with Q)

### A 3.3: Vortrag

### Montag, 18. März 2013, 11:45–12:00, F 128

**Accuracy Limits on the Estimation of the Magnetic Field Gradient** — •Iagoba Apellaniz and Philipp Hyllus — University of the Basque Country, P. O. Box 644, E-48080 Bilbao, Spain.

Entanglement between particles is a useful resource for quantum information processing tasks as well as for quantum metrology. For instance, it allows us to have a
metrological accuracy higher than the shot-noise limit. The accuracy in the estimation of the phase shift θ in a Mach-Zehnder Interferometer can be improved by a factor of √*N* with respect to the shot-noise limit, Δθ∼ 1/√*N*, where *N* is the number of particles on the system which are analyzed to estimate θ.

The usefulness of a multi-particle system for measuring the magnetic field gradient is investigated in Ref. [1]. They consider a multi-particle singlet state for this purpose and incorporate the information about the particle positions in the Hamiltonian.

In our presentation, we use a general Hamiltonian for this class of systems, and the information about the position of the particles involved is encoded in the state, not the Hamiltonian.

We investigate bounds on the sensitivity of measuring the magnetic field gradient, *b*_{1}, with a one dimensional *N*-particle system. We use the so-called Cramér-Rao bound and the Quantum Fisher Information (QFI) in order to get the bounds for the shot-noise limit and the Heisenberg limit.

[1] I. Urizar-Lanz, P. Hyllus, I. Egusquiza, M.W. Mitchell, G. Tóth, *Macroscopic singlet states for gradient magnetometry*, arxiv:1203.3797.