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arXiv:2501.00771

Role of long-range interaction in critical quantum metrology

Zhen-Xia Niu, Wang, Qian

Published Jan 1, 2025• 0 citations
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Abstract

Long-range interacting quantum systems are useful for improving the performance of various applications of quantum technologies. In this work, we carry out a detailed analysis of how the long-range interaction affects the measurement precision in critical quantum metrology. By employing the paradigmatic model of a Kiteav chain with power-law decaying interaction, we focus on the impacts of long-range interaction on the critical sensing for the scenarios with and without uncertainty in system parameters.We show that the long-range interaction can be used as a valuable resource for enhancing the sensitivity of critical parameter estimation in both scenarios. Our findings not only provide more insights into the features of the long-range interacting systems, but also verify the usefulness of long-range interacting systems in quantum metrology.

DOI
10.48550/arxiv.2501.00771

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Long-range interacting quantum systems are useful for improving the performance of various applications of quantum technologies. In this work, we carry out a detailed analysis of how the long-range interaction affects the measurement precision in critical quantum metrology. By employing the paradigmatic model of a Kiteav chain with power-law decaying interaction, we focus on the impacts of long-range interaction on the critical sensing for the scenarios with and without uncertainty in system parameters.We show that the long-range interaction can be used as a valuable resource for enhancing the sensitivity of critical parameter estimation in both scenarios. Our findings not only provide more insights into the features of the long-range interacting systems, but also verify the usefulness of long-range interacting systems in quantum metrology.
Abstract Long-range interacting quantum systems are useful for improving the performance of various applications of quantum technologies. In this work, we carry out a detailed analysis of how the long-range interaction affects the measurement precision in critical quantum metrology. We focus on the ground state, as it not only provides a theoretical foundation for studying dynamical critical quantum metrology, but also has great potential for practical applications. By employing the paradigmatic model of a Kitaev chain with power-law decaying interaction, we investigate the impacts of long-range interaction on the critical sensing for the scenarios with and without uncertainty in system parameters. We show that the long-range interaction can be used as a valuable resource for enhancing the sensitivity of critical parameter estimation in both scenarios. Our findings not only provide more insights into the features of the long-range interacting systems, but also verify the usefulness of long-range interacting systems in quantum metrology
Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the parameters of the Hamiltonian. In realistic settings, there is always some degree of uncertainty in the control parameters used to tune the system to criticality. These uncertainties, while not the target of estimation, can significantly affect the attainable precision, effectively acting as nuisance parameters in the estimation process. Despite being a practically relevant source of noise, their impact on critical metrology has been largely overlooked. In this work we present a general framework that interpolates between single- and multiparameter estimation settings, enabling a systematic analysis of how such uncertainties influence sensitivity. We apply this framework to the paradigmatic transverse field Ising and Lipkin-Meshkov-Glick models, explicitly demonstrating how uncertainty in control parameters affects the metrological performance of critical sensors. For finite-size systems, we identify a fundamental trade-off between robustness to uncertainty and the ability to retain a quantum advantage at the critical point. Our results contribute to a deeper understanding of the practical limitations of critical quantum metrology and provide a route toward its more resilient implementation.
In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology.
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.
Quantum metrology leverages the unique properties of quantum systems to enhance parameter estimation beyond classical limits. In this short review, we introduce the core concepts of quantum metrology, with a particular focus on its extension to multi-parameter estimation. We begin by outlining the foundational principles of quantum metrology and explore how quantum criticality can enhance measurement precision — especially near quantum phase transitions, where systems exhibit heightened sensitivity to external perturbations. Next, we consider the framework of multi-parameter quantum critical metrology, in which the simultaneous estimation of multiple parameters near criticality can lead to further improvements in accuracy. Finally, we discuss measurement-induced phase transitions, a phenomenon emerging in the context of continuous quantum measurements that introduces non-Hermitian dynamics and fundamentally alters the system’s behavior. This review provides a concise overview of these key developments and highlights their significance for future progress in quantum sensing technologies.
Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.