Phase space geometry and optimal state preparation in quantum metrology with collective spins

Abstract

We revisit well-known protocols in quantum metrology using collective spins and propose a unifying picture for optimal state preparation based on a semiclassical description in phase space. We show how this framework allows for quantitative predictions of the timescales required to prepare various metrologically useful states, and that these predictions remain accurate even for moderate system sizes, surprisingly far from the classical limit. Furthermore, this framework allows us to build a geometric picture that relates optimal (exponentially fast) entangled probe preparation to the existence of separatrices connecting saddle points in phase space. We illustrate our results with the paradigmatic examples of the two-axis counter-twisting and twisting-and-turning Hamiltonians, where we provide analytical expressions for all the relevant optimal time scales. Finally, we propose a generalization of these models to include $p$-body collective interaction (or $p$-order twisting), beyond the usual case of $p=2$. Using our geometric framework, we prove a no-go theorem for the local optimality of these models for $p>2$.

15 pages, 6 figures, 9 pages appendix

References in corpus (58)

• Quantum sensing
• Advances in Quantum Metrology
• Quantum metrology
• Quantum metrology with nonclassical states of atomic ensembles
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Quantum spin squeezing
• Quantum metrology from a quantum information science perspective
• Phase space representation of quantum dynamics
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Entanglement and Extreme Spin Squeezing
• Fisher Information and entanglement of non-Gaussian spin states
• Optimal states and almost optimal adaptive measurements for quantum interferometry
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Many particle entanglement in two-component Bose-Einstein Condensates
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Generalized Geometric Quantum Speed Limits
• Approaching the Heisenberg limit without single-particle detection
• Quantum Metrology: Dynamics vs. Entanglement
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Does scrambling equal chaos?
• Entanglement entropy in the Lipkin-Meshkov-Glick model
• Scrambling and entanglement spreading in long-range spin chains
• Loschmidt Echo for quantum metrology
• Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
• Entanglement dynamics in the Lipkin-Meshkov-Glick model
• Quantum critical metrology
• Quantum metrology in Lipkin-Meshkov-Glick critical systems
• Optimal and Robust Quantum Metrology Using Interaction-Based Readouts
• Near-Unitary Spin Squeezing in ${}^{171}$Yb
• Excited-state quantum phase transitions
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Quantum-limited metrology with product states
• Nonlinear quantum metrology of many-body open systems
• Quantum metrology with a quantum-chaotic sensor
• On quantum mean-field models and their quantum annealing
• Origin of the slow growth of entanglement entropy in long-range interacting spin systems
• Dissipative Quantum Metrology with Spin Cat States
• Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator
• Collective Spin-Light and Light-Mediated Spin-Spin Interactions in an Optical Cavity
• A generalized phase space approach for solving quantum spin dynamics
• Quantum phase transitions in fully connected spin models: an entanglement perspective
• Phase magnification by two-axis countertwisting for detection noise robust interferometry
• Robustifying Twist-and-Turn Entanglement with Interaction-Based Readout
• Saddle-point scrambling without thermalisation
• Dynamical and excited-state quantum phase transitions in collective systems
• How do wave packets spread? Time evolution on Ehrenfest time scales
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Strongly Enhanced Spin Squeezing via Quantum Control
• Fast and optimal generation of entanglement in bosonic Josephson junctions
• Diverging quantum speed limits: a herald of classicality
• States for phase estimation in quantum interferometry
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing
• Simulation of complex dynamics of mean-field $p$-spin models using measurement-based quantum feedback control
• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• Non-equilibrium and non-homogeneous phenomena around a first-order quantum phase transition
• Precision Measurements Using Squeezed Spin States via Two-axis Counter-twisting Interactions
• Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atomic interferometry

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