Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic optimality of twist-untwist protocols for Heisenberg scaling
  in atomic interferometry   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.

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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat