Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
arXiv:2509.12579 · doi:10.1126/sciadv.adk7616
Abstract
Non-Hermitian quantum metrology, an emerging field at the intersection of quantum estimation and non-Hermitian physics, holds promise for revolutionizing precision measurement. Here, we present a comprehensive investigation of non-Hermitian quantum parameter estimation in the quantum regime, with a special focus on achieving Heisenberg scaling. We introduce a concise expression for the quantum Fisher information (QFI) that applies to general non-Hermitian Hamiltonians, enabling the analysis of estimation precision in these systems. Our findings unveil the remarkable potential of non-Hermitian systems to attain the Heisenberg scaling of , where represents time. Moreover, we derive optimal measurement conditions based on the proposed QFI expression, demonstrating the attainment of the quantum Cramér-Rao bound. By constructing non-unitary evolutions governed by two non-Hermitian Hamiltonians, one with parity-time symmetry and the other without specific symmetries, we experimentally validate our theoretical analysis. The experimental results affirm the realization of Heisenberg scaling in estimation precision, marking a substantial milestone in non-Hermitian quantum metrology.
arXiv comment48 pages, 15 figures
References in corpus (51)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Quantum-enhanced measurements: beating the standard quantum limit
- Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
- Quantum metrology
- Complex Extension of Quantum Mechanics
- Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
- On the Improvement of Frequency Stardards with Quantum Entanglement
- Topological energy transfer in an optomechanical system with exceptional points
- PT-symmetry breaking and laser-absorber modes in optical scattering systems
- PT-symmetric laser-absorber
- Quantum metrology from a quantum information science perspective
- Beating the Standard Quantum Limit with Four Entangled Photons
- The elusive Heisenberg limit in quantum enhanced metrology
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Entanglement-free Heisenberg-limited phase estimation
- Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
- Metrology with -symmetric cavities: Enhanced sensitivity near the -phase transition
- Quantum enhanced measurements without entanglement
- Observation of parity-time symmetry breaking in a single spin system
- Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer
- Faster than Hermitian Quantum Mechanics
- Quantum state tomography across the exceptional point in a single dissipative qubit
- Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
- Quantum Noise Theory of Exceptional Point Sensors
- The General Quantum Interference Principle and the Duality Computer
- Achieving the Heisenberg limit in quantum metrology using quantum error correction
- Entanglement-enhanced measurement of a completely unknown phase
- Information Retrieval and Criticality in Parity-Time-Symmetric Systems
- Observation of critical phenomena in parity-time-symmetric quantum dynamics
- The Naimark dilated PT-symmetric brachistochrone
- Mixed-state evolution in the presence of gain and loss
- Quantum metrology for a general Hamiltonian parameter
- Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
- Observation of Fast Evolution in Parity-Time-Symmetric System
- Dynamically encircling an exceptional point in a real quantum system
- Adaptive quantum metrology under general Markovian noise
- Effective spontaneous PT-symmetry breaking in hybridized metamaterials
- Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms
- Universal time scaling for Hamiltonian parameter estimation
- Beating the standard quantum limit: Phase super-sensitivity of N-photon interferometers
- Observation of -symmetric quantum coherence in a single ion system
- Measuring Non-Hermitian Operators via Weak Values
- Control-enhanced sequential scheme for general quantum parameter estimation at the Heisenberg limit
- Optimized heat transfer at exceptional points in quantum circuits
- Optimal Strategies of Quantum Metrology with a Strict Hierarchy
- Tighter Uncertainty and Reverse Uncertainty Relations
- Information Geometry of Complex Hamiltonians and Exceptional Points
- Products of weak values: uncertainty relations, complementarity and incompatibility
- Strong unitary uncertainty relations
- Quantum Fisher Information Perspective on Sensing in Anti-PT Symmetric Systems
- Quantum parameter estimation of non-Hermitian systems with optimal measurements
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- Review: Quantum Metrology and Sensing with Many-Body Systems
- Critical non-Hermitian topology induced quantum sensing
- Factorization dynamics between quantum Fisher information and quantum coherence
- Three perspectives on entropy dynamics in a non-Hermitian two-state system
- Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors
- Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
- Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
- Critical quantum metrology robust against dissipation and non-adiabaticity
- Persistent quantum advantage with definite photon-number states in lossy multiple-phase estimation
- Heisenberg scaling based on population coding
- Topological Sensing in the Dynamics of Quantum Walks with Defects
- Noisy Stark probes as quantum-enhanced sensors
- Approaching the Multiparameter Quantum Cramér-Rao Bound via Classical Correlation and Entangling Measurements
- Towards Robust Optimal Measurements Against Noise in Quantum Metrology