Quantum-enhanced sensing from the interplay of long-range interactions and non-Hermiticity

TL;DR

This paper explores how long-range interactions and non-Hermiticity in quantum spin systems can enhance parameter estimation, showing improved quantum Fisher information scaling and metrological advantages.

Contribution

It demonstrates that tuning long-range interactions and non-Hermitian effects can improve quantum sensing performance compared to short-range and Hermitian models.

Findings

Enhanced QFI scaling in long-range regimes

Non-Hermitian models can outperform Hermitian counterparts in QFI

No advantage at critical magnetic field with eigenstate initialization

Abstract

Long-range (LR) quantum spin systems offer promising advantages for quantum information processing and sensing. Here, we investigate parameter estimation in an long-range XX spin model coupled to a reservoir, which gives rise to an effective long-range RT-symmetric non-Hermitian iXY Hamiltonian. The interactions extend up to a tunable coordination range and decay algebraically with distance, enabling a direct comparison between long-range and short-range (SR) regimes. Focusing on the estimation of the transverse magnetic field and anisotropy parameter, we initialize the system in a fully polarized state and analyze the resulting dynamical quantum Fisher information (QFI). We show that, with suitable tuning of the system parameters, both the time and system-size scaling of the QFI are enhanced in the LR regime relative to their SR counterparts. Moreover, the non-Hermitian LR model can exhibit superior dynamical QFI compared with the corresponding Hermitian model, demonstrating a genuine metrological advantage induced by the interplay of long-range interactions and non-Hermitian effects. In contrast, we establish a no-go result at the critical magnetic field: when the probe is prepared in the lowest-energy eigenstate, the QFI scaling remains identical for the Hermitian and non-Hermitian cases.