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.

arXiv comment8 pages, 2 figures

References in corpus (35)

• Quantum metrology
• Quantum metrology with nonclassical states of atomic ensembles
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Quantum spin squeezing
• Direct Observation of Second Order Atom Tunnelling
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Three-dimensional Roton-Excitations and Supersolid formation in Rydberg-excited Bose-Einstein Condensates
• Entanglement and Extreme Spin Squeezing
• Entangling Atomic Spins with a Strong Rydberg-Dressed Interaction
• Approaching the Heisenberg limit without single-particle detection
• Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics
• Quantum amplification of mechanical oscillator motion
• Quantum state magnification
• Collective many-body interaction in Rydberg dressed atoms
• Reduced back-action for phase sensitivity 10 times beyond the standard quantum limit
• Time-Reversal-Based Quantum Metrology with Many-Body Entangled States
• Interactions Between Rydberg-Dressed Atoms
• Loschmidt Echo for quantum metrology
• Spin squeezing in a Rydberg lattice clock
• Variational spin-squeezing algorithms on programmable quantum sensors
• Near-optimal quantum circuit for Grover's unstructured search using a transverse field
• Entanglement interferometry for precision measurement of atomic scattering properties
• Optimal and Robust Quantum Metrology Using Interaction-Based Readouts
• Near-Unitary Spin Squeezing in ${}^{171}$Yb
• Metrological Nonlinear Squeezing Parameter
• Trapped Ion Quantum Information Processing with Squeezed Phonons
• Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing
• 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
• Ramsey interferometry with generalized one-axis twisting echoes
• Using Interaction-Based Readouts to Approach the Ultimate Limit of Detection Noise Robustness for Quantum-Enhanced Metrology in Collective Spin Systems
• Robustifying Twist-and-Turn Entanglement with Interaction-Based Readout
• Noise-resistant optimal spin squeezing via quantum control
• Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians

Cited by in corpus (5)

• Phase space geometry and optimal state preparation in quantum metrology with collective spins
• Entanglement-Enhanced Optical Atomic Clocks
• Optimal Ramsey interferometry with echo protocols based on one-axis twisting
• Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout
• Globally optimal interferometry with lossy twin Fock probes