Quantum Fisher information from randomized measurements
arXiv:2105.13164 · doi:10.1103/PhysRevLett.127.260501
Abstract
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement in quantum many-body-systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
arXiv comment7 + 10 pages with 3 + 3 figures. Accepted version with additional analytical expressions for statistical errors of arbitrary order polynomials of the density matrix estimated via classical shadows. Code available at https://github.com/bvermersch/RandomMeas
References in corpus (62)
- Quantum Computing in the NISQ era and beyond
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- Quantum metrology with nonclassical states of atomic ensembles
- Predicting Many Properties of a Quantum System from Very Few Measurements
- 14-qubit entanglement: creation and coherence
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Probing entanglement entropy via randomized measurements
- Fisher information and multiparticle entanglement
- Multipartite entanglement and high precision metrology
- Quantum spin dynamics and entanglement generation with hundreds of trapped ions
- Fisher Information and entanglement of non-Gaussian spin states
- Observation of multi-component atomic Schrödinger cat states of up to 20 qubits
- Evenly distributed unitaries: on the structure of unitary designs
- Taming multiparticle entanglement
- Quantum criticality as a resource for quantum estimation
- Mixed-state entanglement from local randomized measurements
- Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
- Bell Correlations in a Bose-Einstein Condensate
- Symmetry-resolved entanglement detection using partial transpose moments
- Efficient estimation of Pauli observables by derandomization
- Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions
- Sample-optimal tomography of quantum states
- Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
- Cross-Platform Verification of Intermediate Scale Quantum Devices
- The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
- Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
- Robust shadow estimation
- Verifying Multipartite Entangled GHZ States via Multiple Quantum Coherences
- Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
- Multipartite entanglement in topological quantum phases
- Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
- Dynamics of quantum information
- Unitary -designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
- Probing scrambling using statistical correlations between randomized measurements
- Single-copies estimation of entanglement negativity
- Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
- Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
- Many-body topological invariants from randomized measurements
- Random bosonic states for robust quantum metrology
- Metrological Detection of Multipartite Entanglement from Young Diagrams
- Efficient and feasible state tomography of quantum many-body systems
- Number squeezing, quantum fluctuations and oscillations in mesoscopic Bose Josephson junctions
- Optimal Entanglement Certification from Moments of the Partial Transpose
- Characterizing multipartite entanglement with moments of random correlations
- Many-body Chern number from statistical correlations of randomized measurements
- Driven quantum dynamics: will it blend?
- Experimental estimation of the quantum Fisher information from randomized measurements
- Detecting metrologically useful asymmetry and entanglement by a few local measurements
- Bound entanglement from randomized measurements
- Multipartite Entanglement Analysis From Random Correlations
- Noise in Bose Josephson junctions: Decoherence and phase relaxation
- Witnessing multipartite entanglement by detecting asymmetry
- Importance sampling of randomized measurements for probing entanglement
- Mesoscopic quantum superpositions in bimodal Bose-Einstein condensates: decoherence and strategies to counteract it
- Entanglement characterization using quantum designs
- Sub-Quantum Fisher Information
- Macroscopic superpositions in Bose-Josephson junctions: Controlling decoherence due to atom losses
- Intrinsic metrological resolution as a distance measure and nonclassical light
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- QuanEstimation: An open-source toolkit for quantum parameter estimation
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- A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator
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- Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
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