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Non-commutativity as a Universal Characterization for Enhanced Quantum Metrology
Authors:
Ningxin Kong,
Haojie Wang,
Mingsheng Tian,
Yilun Xu,
Geng Chen,
Yu Xiang,
Qiongyi He
Abstract:
A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index $\mathcal{K}$, which quantifies the depth of non…
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A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index $\mathcal{K}$, which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite $\mathcal{K}$ yields an enhanced scaling of root-mean-square error as $N^{-(1+\mathcal{K})}$. Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit $\mathcal{K} \to \infty$, exponential precision scaling $N^{-1}e^{-N}$ is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.
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Submitted 27 November, 2025;
originally announced November 2025.
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Exceptional-Point-Induced Nonequilibrium Entanglement Dynamics in Bosonic Networks
Authors:
Chenghe Yu,
Mingsheng Tian,
Ningxin Kong,
Matteo Fadel,
Xinyao Huang,
Qiongyi He
Abstract:
Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogo…
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Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer-pi hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.
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Submitted 6 February, 2025;
originally announced February 2025.
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Manipulating Spectral Windings and Skin Modes through Nonconservative Couplings
Authors:
Ningxin Kong,
Chenghe Yu,
Yilun Xu,
Matteo Fadel,
Xinyao Huang,
Qiongyi He
Abstract:
The discovery of the non-Hermitian skin effect (NHSE) has revolutionized our understanding of wave propagation in non-Hermitian systems, highlighting unexpected localization effects beyond conventional theories. Here, we discover that NHSE, accompanied by multitype spectral phases, can be induced by manipulating nonconservative couplings. By characterizing the spectra through the windings of the e…
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The discovery of the non-Hermitian skin effect (NHSE) has revolutionized our understanding of wave propagation in non-Hermitian systems, highlighting unexpected localization effects beyond conventional theories. Here, we discover that NHSE, accompanied by multitype spectral phases, can be induced by manipulating nonconservative couplings. By characterizing the spectra through the windings of the energy bands, we demonstrate that band structures with identical, opposite, and even twisted windings can be achieved. These inequivalent types of spectra originate from the multichannel interference resulting from the interplay between conservative and nonconservative couplings. Associated with the multitype spectra, unipolar and bipolar NHSE with different eigenmode localizations can be observed. Additionally, our findings link the nonreciprocal transmission properties of the system to multiple spectral phases, indicating a connection with the skin modes. This paper paves new pathways for investigating non-Hermitian topological effects and manipulating nonreciprocal energy flow.
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Submitted 13 November, 2024; v1 submitted 21 June, 2024;
originally announced June 2024.