Achieving the Heisenberg limit with Dicke states in noisy quantum metrology

TL;DR

This paper demonstrates that Dicke states can be used in noisy quantum metrology to surpass the standard quantum limit and reach the Heisenberg limit, even with decay effects, by analyzing quantum Fisher information in open quantum systems.

Contribution

It introduces a method using Dicke states to achieve Heisenberg-limited precision in noisy quantum systems, outperforming GHZ and separable states under certain conditions.

Findings

Dicke states enable surpassing the standard quantum limit in noisy systems.

Optimal excitation Dicke states can reach the Heisenberg limit despite decay.

Separable states can outperform GHZ states under specific noise conditions.

Abstract

Going beyond the standard quantum limit in noisy quantum metrology is an important and challenging task. Here we show how Dicke states can be used to surpass the standard quantum limit and achieve the Heisenberg limit in open quantum systems. The system we study has qubits symmetrically coupled to a resonator and our objective is to estimate the coupling between the qubits and the resonator. The time-dependent quantum Fisher information with respect to the coupling is studied for this open quantum system where the same decay rates are assumed on all qubits. We show that when the system is initialized to a Dicke state with an optimal excitation number one can go beyond the standard quantum limit and achieve the Heisenberg limit even for finite values of the decays on the qubit and the resonator, particularly when the qubits and resonator are strongly coupled. We compare our results against the highly entangled GHZ state and a completely separable state and show that the GHZ state performs quite poorly whereas under certain noise conditions the separable state is able to go beyond the standard quantum limit due to subsequent interactions with a resonator.