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arXiv:2605.01912

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

Keshav Das Agarwal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, Aditi Sen De

quant-phcond-mat.str-elSubmitted May 3, 2026• Announced May 5, 2026• 0 citations
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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.

Comments
13 pages, 9 figures

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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.
The non-Hermitian transverse XYXYXY model with Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interaction having RT\mathcal{RT}RT-symmetry, referred to as iKSEAiKSEAiKSEA model, possesses both an exceptional point at which eigenvectors coalesce and a quantum critical point where gap-closing occurs. To precisely estimate the magnetic field of the system, we prove that the quantum Fisher information (QFI) of the ground state of the iKSEAiKSEAiKSEA model, which is a lower bound of the precision quantified by the root mean square error, scales as N2N^2N2, with NNN being the system-size. This provides Heisenberg scaling both at the quantum critical point and the exceptional point in the thermodynamic limit. It indicates that reservoir engineering can provide enhanced precision of system parameters when the system is in contact with the bath, resulting in this non-Hermitian model. Additionally, we demonstrate analytically that, in contrast to Hermitian systems, QFI surpasses the Heisenberg limit and achieves super-Heisenberg scaling (∼N6\sim N^6∼N6), when the strength of the KSEA interaction approaches the anisotropy parameter, permitting competition between non-hermiticity and hermiticity features, as long as the system size is moderate. Moreover, we illustrate that starting from a product state, the non-Hermitian evolving Hamiltonian can create the dynamical state that surpasses the standard quantum limit in the broken regime.
Going beyond short-range interactions, we explore the role of long-range interactions in the extended XY model for transferring quantum states through evolution. In particular, employing a spin-1/2 chain with interactions decaying as a power law, we demonstrate that long-range (LR) interactions significantly enhance the efficiency of a quantum state transfer (QST) protocol, improving the achievable fidelity, mitigating its slow decline as compared with the nearest-neighbor setting, associated with increasing system-size. Our study identifies the LR regime as providing an optimal balance between interaction range and transfer efficiency, outperforming the protocol with the short-range interacting model. Our detailed analysis reveals the impact of system parameters, such as anisotropy, magnetic field strength, and coordination number, on QST dynamics. Specifically, we find that intermediate coordination numbers lead to a faster and more reliable state transfer, while extreme values diminish performance. Furthermore, we exhibit that the presence of LR interactions considerably reduces the minimum time required to achieve fidelity beyond the classical limit.
Quantum Fisher Information (QFI) is a fundamental quantity in quantum parameter estimation theory, characterizing the ultimate precision bound of parameter estimation. In this work, we investigate QFI for quantum states in non-Hermitian systems. By employing the projected Hilbert space method and spectral decomposition, we derive an explicit expression for the QFI in terms of the density matrix and parameter generators. This formulation not only recovers the well-known results in the Hermitian case but also captures the non-Hermitian effects induced by the time-dependent norm of the state. To validate our theoretical framework, we analyze a single-qubit pseudo-Hermitian system and apply Naimark dilation theory to embed it into an equivalent Hermitian system. The comparison between the original and dilated systems demonstrates the consistency and applicability of the proposed QFI formula in non-Hermitian settings. In addition, we investigate a PT\mathcal{PT}PT-symmetric system to further explore the influence of non-Hermiticity on QFI. Our findings offer a new perspective for analyzing and enhancing QFI in non-Hermitian systems, paving the way for promising applications in non-Hermitian quantum metrology and sensing.
The typical bound on parameter estimation, known as the standard quantum limit (SQL), can be surpassed by exploiting quantum resources such as entanglement. To estimate the magnetic probe field, we propose a quantum sensor based on a variable-range many-body quantum spin chain with a moderate transverse magnetic field. We report the threefold benefits of employing a long-range system as a quantum sensor. First, sensors with quasi-long-range interactions can always beat the SQL for all values of the coordination number, while a sensor with long-range interactions does not have this ubiquitous quantum advantage. Second, a long-range Hamiltonian outperforms a nearest-neighbor (NN) Hamiltonian in terms of both estimating precision and system-size scaling. Finally, we observe that the system with long-range interactions can go below the SQL in the presence of a high temperature of the initial state, while sensors having NN interactions cannot. Furthermore, a sensor based on the long-range Ising Hamiltonian proves to be robust against impurities in the magnetic field and when the time-inhomogeneous dephasing noise acts during interaction of the probe with the system.
We theoretically investigate quantum parameter estimation in a two-qubit anisotropic Heisenberg spin system with Dzyaloshinskii-Moriya (DM) interaction in the presence of intrinsic decoherence described by the Milburn model. Using the Quantum Fisher Information (QFI), we study the estimation of both the uniform magnetic field and the DM interaction strength. Analytical expressions for the time-evolved density matrix are obtained and used to explore the effects of exchange anisotropy, intrinsic decoherence, and probe-state preparation on the achievable estimation precision. Our results show that suitable tuning of the anisotropic exchange coupling and the initial entangled state can considerably enhance the estimation performance, with different optimal parameter regimes emerging for magnetic-field and DM-interaction sensing. To better understand the role of quantum resources in metrology, we also examine the behaviour of concurrence, quantum coherence, and von Neumann entropy. Overall, our findings demonstrate that anisotropic Heisenberg spin systems with DM interaction provide a promising and flexible platform for high-precision quantum metrology even in the presence of intrinsic decoherence.
With optimal control theory, we compute the maximum possible quantum Fisher information about the interaction parameter for a Kitaev chain with tunable long-range interactions in the many-particle Hilbert space. We consider a wide class of decay laws for the long-range interaction and develop rigorous asymptotic analysis for the scaling of the quantum Fisher information with respect to the number of lattice sites. In quantum metrology nonlinear many-body interactions can enhance the precision of quantum parameter estimation to surpass the Heisenberg scaling, which is quadratic in the number of lattice sites. Here for the estimation of the long-range interaction strength, we observe the Heisenberg to super-Heisenberg transition in such a linearlinearlinear model, related to the slow decaying long-range correlations in the model. Finally, we show that quantum control is able to improve the prefactor rather than the scaling exponent of the quantum Fisher information. This is in contrast with the case where quantum control has been shown to improve the scaling of quantum Fisher information with the probe time. Our results clarify the role of quantum controls and long-range interactions in many-body quantum metrology.