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- W4221093060 abstract "Twist-untwist protocols for quantum metrology consist of a serial application of: 1. unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), 2. parameterized dynamics $U(phi)$ (e.g., a collective rotation or phase space displacement), 3. time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of $phi$ even when the nonlinearities are applied for times much shorter than required to produce Schr{o}dinger cat states. In this work, we prove that twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only measurement of a spin operator $vec{n}cdot vec{J}$, asymptotically in the number of particles. We consider the following physical settings: all-to-all interactions generated by one-axis twisting $J_{z}^{2}$ (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve $85%$ and $92%$ of the respective quantum Cram'{e}r-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of $L$ without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an $L$ layer quantum alternating operator ansatz." @default.
- W4221093060 created "2022-04-03" @default.
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- W4221093060 date "2022-03-28" @default.
- W4221093060 modified "2023-09-25" @default.
- W4221093060 title "Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atom-based sensing" @default.
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- W4221093060 doi "https://doi.org/10.1103/physrevresearch.4.013236" @default.
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