Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atomic interferometry

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 $U(\varphi )$ (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 $\varphi$ even when the nonlinearities are applied for times much shorter than required to produce Schrödinger 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 Cramér-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.

8 pages, 2 figures

References in corpus (6)

• Time-Reversal-Based Quantum Metrology with Many-Body Entangled States
• Near-Unitary Spin Squeezing in ${}^{171}$Yb
• Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
• Stroboscopic qubit measurement with squeezed illumination
• One- and two-axis squeezing of atomic ensembles in optical cavities
• Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians

Cited by in corpus (5)

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• Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout
• Globally optimal interferometry with lossy twin Fock probes