Nonlinear quantum metrology of many-body open systems

Abstract

We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a $k$-body Hamiltonian and $p$-body Lindblad operators, the estimation error of a Hamitonian parameter using a Greenberger-Horne-Zeilinger (GHZ) state as a probe is shown to scale as $N^{-\left(k-\frac{p}{2}\right)}$, surpassing the shot-noise limit for $2k>p+1$. Metrology equivalence between initial product states and maximally entangled states is established for $p\ge 1$. We further show that one can estimate the system-environment coupling parameter with precision $N^{-\frac{p}{2}}$, while many-body decoherence enhances the precision to $N^{-k}$ in the noise-amplitude estimation of a fluctuating $k$-body Hamiltonian. For the long-range Ising model we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

5+9 pp, 1 figure

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• An Open-System Quantum Simulator with Trapped Ions
• Quantum speed limits in open system dynamics
• Generalized Limits for Single-Parameter Quantum Estimation
• Using entanglement against noise in quantum metrology
• Quantum Metrology: Dynamics vs. Entanglement
• Quantum Metrological Limits via a Variational Approach
• Quantum-limited metrology with product states
• A nonlinear Ramsey interferometer operating beyond the Heisenberg limit
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Quantum limited measurements of atomic scattering properties
• Quantum Metrology: Extended Convexity of Quantum Fisher Information

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