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arXiv · 2405.15703

Metrological usefulness of entanglement and nonlinear Hamiltonians

Satoya Imai·Augusto Smerzi·Luca Pezzè
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Abstract

A central task in quantum metrology is to exploit quantum correlations to outperform classical sensitivity limits. Metrologically useful entanglement is identified when the quantum Fisher information (QFI) exceeds a separability bound for a given parameter-encoding Hamiltonian. However, so far, only results for linear Hamiltonians are well-established. Here, we characterize metrologically useful entanglement for nonlinear Hamiltonians, presenting separability bounds for collective angular momenta. Also, we provide a general expression for entangled states maximizing the QFI, which can be written as the superposition between the GHZ-like and singlet states. Finally, we compare the metrological usefulness of linear and nonlinear cases, in terms of entanglement detection and random symmetric states.

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Satoya Imai, Augusto Smerzi, Luca Pezzè. 2024-05-24. Metrological usefulness of entanglement and nonlinear Hamiltonians. https://doi.org/10.1103/physreva.111.l020402

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