Parameter estimation in the presence of the most general Gaussian dissipative reservoir

TL;DR

This paper investigates the fundamental limits of quantum parameter estimation when dealing with the most general Gaussian dissipative reservoirs, revealing the impossibility of asymptotic Heisenberg limit achievement but identifying conditions for Heisenberg-limited performance with fixed probes.

Contribution

It derives bounds on phase and frequency estimation precision in Gaussian dissipative environments and discusses a realistic cavity-based implementation.

Findings

Heisenberg limit cannot be asymptotically achieved with such reservoirs.

For fixed probe numbers, Heisenberg-limited performance is theoretically possible.

A practical frequency estimation scheme in a cavity system is proposed.

Abstract

We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency estimation. For both problems we show that it is impossible to achieve the Heisenberg limit asymptotically in the presence of such a reservoir. However, we also find that for any fixed number of probes used in the setup there exists a Gaussian dissipative reservoir, which, in principle, allows for the Heisenberg-limited performance for that number of probes. We discuss a realistic implementation of a frequency estimation scheme in the presence of a Gaussian dissipative reservoir in a cavity system.