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New Journal of Physics

Role of interaction range in critical quantum metrology for long-range Kitaev chain

Zhen-Xia Niu, Qian Wang

Published Dec 22, 2025• 2 citations
Publisher

Abstract

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

DOI
10.1088/1367-2630/ae3026

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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. 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
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.
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.
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.
We investigate the signature of quantum criticality in the long-time stationary state of the long-range Kitaev chain by performing various quench protocols. In this model, the pairing interaction decays with distance according to a power law with exponent $\ensuremath{\alpha}$. Using quantum information-theoretic measures, such as mutual information and logarithmic negativity, we show that irrespective of the values of $\ensuremath{\alpha}$, critical-to-critical quench displays quantum criticality even in the stationary state. Remarkably, in the presence of long-range pairing interactions, where fermionic correlators decay algebraically even at noncritical points, the signature of quantum criticality persists in the stationary state. Furthermore, the effective central charge, calculated from both mutual information and logarithmic negativity of the stationary state following a critical-to-critical quench, agrees with the central charge of the corresponding ground states for both $\ensuremath{\alpha}=0$ and $\ensuremath{\alpha}=2$. Therefore, information of the universality class can be inferred from the stationary state.
We investigate the signature of quantum criticality in the long-time stationary state of the long-range Kitaev chain by performing various quench protocols. In this model, the pairing interaction decays with distance according to a power law with exponent ααα. Using quantum information-theoretic measures, such as mutual information and logarithmic negativity, we show that, irrespective of the values of ααα, critical-to-critical quench displays quantum criticality even in the stationary state. Remarkably, in the presence of long-range pairing interactions, where fermionic correlators decay algebraically even at non-critical points, signature of quantum criticality persists in the stationary state. Furthermore, the effective central charge, calculated from both mutual information and logarithmic negativity of stationary state following a critical-to-critical quench, agrees with the central charge of the corresponding ground states for both α=0α= 0α=0 and α=2α= 2α=2. Therefore, information of the universality class can be inferred from the stationary state.
We study the role of long-range interactions (more precisely, the long-range superconducting gap term) on the nonequilibrium dynamics considering a long-range ppp-wave superconducting chain in which the superconducting term decays with distance between two sites in a power-law fashion characterized by an exponent $\ensuremath{\alpha}$. We show that the Kibble-Zurek scaling exponent, dictating the power-law decay of the defect density in the final state reached following a slow (in comparison to the time scale associated with the minimum gap in the spectrum of the Hamiltonian) quenching of the chemical potential $\ensuremath{\mu}$ across a quantum critical point, depends nontrivially on the exponent $\ensuremath{\alpha}$ as long as $\ensuremath{\alpha}<2$; on the other hand, for $\ensuremath{\alpha}>2$, we find that the exponent saturates to the corresponding well-known value of 1/21/21/2 expected for the short-range model. Furthermore, studying the dynamical quantum phase transitions manifested in the nonanalyticities in the rate function of the return possibility I(t)I(t)I(t) in subsequent temporal evolution following a sudden change in $\ensuremath{\mu}$, we show the existence of a new region; in this region, we find three instants of cusp singularities in I(t)I(t)I(t) associated with a single sector of Fisher zeros. Notably, the width of this region shrinks as $\ensuremath{\alpha}$ increases and vanishes in the limit $\ensuremath{\alpha}\ensuremath{\rightarrow}2$, indicating that this special region is an artifact of the long-range nature of the Hamiltonian.