Restoring metrological quantum advantage of measurement precision in noisy scenario

TL;DR

This paper demonstrates that quantum advantage in measurement precision can be restored in noisy scenarios by using specific interactions and initial states, with implications for quantum metrology under dephasing noise.

Contribution

It reveals conditions under which quantum advantage can be regained in noisy quantum metrology, especially through Ising interactions and initial entanglement considerations.

Findings

Quantum advantage can be restored with Ising interactions in noisy environments.

Entanglement content affects the precision of coupling constant estimation.

Quantum advantage varies depending on the parameter and interaction considered.

Abstract

We show that in presence of a local and uncorrelated dephasing noise, quantum advantage can be obtained in the Fisher information-based lower bound of the minimum uncertainty in estimating parameters of the system Hamiltonian. The quantum advantage refers here to the benefit of initiating with a maximally entangled state instead of a product one. This quantum advantage was known to vanish in the same noisy scenario for a frequency estimation protocol. Restoration of the better precision in frequency estimation with maximally entangled probes can be obtained by incorporating an interaction between the system particles. The interaction examined here is Ising in nature, and is considered with or without a transverse magnetic field. There are instances, e.g. where frequency estimation in presence of a transverse field is considered and quantum advantage is not restored. A quantum advantage can also be obtained while estimating the strength of the introduced magnetic field along the transverse direction, whereas for the instances considered, using uncorrelated probes is better in measuring the coupling parameter of the Ising interaction. We also investigate the dependence of measurement precision on the entanglement content, which is not necessarily maximal, of the initial state. The precision in estimation of coupling constant decreases monotonically with the increase of entanglement content of the initial state, while the same for frequency estimation is independent of the entanglement content of the inputs.