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Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

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  • Shengshi Pang

    (University of Rochester
    Center for Coherence and Quantum Optics, University of Rochester)

  • Andrew N. Jordan

    (University of Rochester
    Center for Coherence and Quantum Optics, University of Rochester
    Institute for Quantum Studies, Chapman University)

Abstract

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

Suggested Citation

  • Shengshi Pang & Andrew N. Jordan, 2017. "Optimal adaptive control for quantum metrology with time-dependent Hamiltonians," Nature Communications, Nature, vol. 8(1), pages 1-9, April.
    • Handle: RePEc:nat:natcom:v:8:y:2017:i:1:d:10.1038_ncomms14695
    DOI: 10.1038/ncomms14695
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    Cited by:

    1. Jordyn Hales & Utkarsh Bajpai & Tongtong Liu & Denitsa R. Baykusheva & Mingda Li & Matteo Mitrano & Yao Wang, 2023. "Witnessing light-driven entanglement using time-resolved resonant inelastic X-ray scattering," Nature Communications, Nature, vol. 14(1), pages 1-10, December.

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