Temperature estimation of an entangled pair of trapped ions

TL;DR

This paper presents a method using estimation theory and Fisher matrix formalism to infer the temperature of entangled trapped ions' vibrational modes, optimizing interaction time and leveraging non-classical states for improved accuracy.

Contribution

It introduces a novel scheme for temperature estimation of entangled trapped ions using only local measurements and considers effects of non-thermal reservoirs.

Findings

Optimized interaction time enhances temperature inference accuracy.

Non-classical states improve the estimation of individual ion temperatures.

The method effectively infers temperatures using measurements on a single ion.

Abstract

We apply estimation theory to a system formed by two interacting trapped ions. By using the Fisher matrix formalism, we introduce a simple scheme for estimation of the temperature of the longitudinal vibrational modes of the ions. We use the ions interaction to effectively infer the temperature of the individual ions, by optimising the interaction time evolution and by measuring only over one of the ions. We also investigate the effect of a non-thermal reservoir over the inference approach. The non-classicality of one of the ions vibrational modes, introduced due to a squeezed thermal reservoir, improves the indirect inference of the individual temperatures.