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arXiv · 1612.05237

Nonlinear quantum metrology of many-body open systems

Mathieu Beau·Adolfo del Campo
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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 $p\geq 1$. 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.

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Mathieu Beau, Adolfo del Campo. 2016-12-15. Nonlinear quantum metrology of many-body open systems. https://doi.org/10.1103/physrevlett.119.010403

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