Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime

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 $1/t$, where $t$ 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.

48 pages, 15 figures

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• Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors
• 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