Quantum probes for the cutoff frequency of Ohmic environments

TL;DR

This paper investigates how quantum probes, including single and two-qubit systems, can be used to accurately estimate the cutoff frequency of an Ohmic environment, revealing conditions where simple probes are optimal and others where entangled probes offer advantages.

Contribution

It demonstrates that single-qubit probes are generally optimal for estimating the cutoff frequency in Ohmic environments, with specific conditions where two-qubit entangled probes outperform them.

Findings

Single-qubit probes are often optimal for cutoff frequency estimation.

Two-qubit Bell states can outperform single-qubit probes under certain conditions.

No improvement in estimation precision with two-qubit probes for most parameter values.

Abstract

Quantum probing consists of suitably exploiting a simple, small, and controllable quantum system to characterize a larger and more complex system. Here, we address the estimation of the cutoff frequency of the Ohmic spectral density of a harmonic reservoir by quantum probes. To this aim, we address the use of single-qubit and two-qubit systems and different kinds of coupling with the bath of oscillators. We assess the estimation precision by the quantum Fisher information of the sole quantum probe as well as the corresponding quantum signal-to-noise ratio. We prove that, for most of the values of the Ohmicity parameter, a simple probe such as a single qubit is already optimal for the precise estimation of the cutoff frequency. Indeed for those values, upon considering a two-qubit probe either in a Bell or in separable state, we do not find improvement to the estimation precision. However, we also showed that there exist few conditions where employing two qubits in a Bell state interacting with a common bath is more suitable for precisely estimating the cutoff frequency.