Quantum Fisher information from randomized measurements

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.

7 + 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 (17)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• 14-qubit entanglement: creation and coherence
• Fisher Information and entanglement of non-Gaussian spin states
• Evenly distributed unitaries: on the structure of unitary designs
• Taming multiparticle entanglement
• Quantum criticality as a resource for quantum estimation
• Symmetry-resolved entanglement detection using partial transpose moments
• Efficient estimation of Pauli observables by derandomization
• Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
• Multipartite entanglement in topological quantum phases
• Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
• Metrological Detection of Multipartite Entanglement from Young Diagrams
• Number squeezing, quantum fluctuations and oscillations in mesoscopic Bose Josephson junctions
• Optimal Entanglement Certification from Moments of the Partial Transpose
• Experimental estimation of the quantum Fisher information from randomized measurements
• Importance sampling of randomized measurements for probing entanglement
• Intrinsic metrological resolution as a distance measure and nonclassical light

Cited by in corpus (25)

• The randomized measurement toolbox
• Learning Quantum Systems
• Avoiding barren plateaus using classical shadows
• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• Entanglement barrier and its symmetry resolution: theory and experiment
• QuanEstimation: An open-source toolkit for quantum parameter estimation
• Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Optimising shadow tomography with generalised measurements
• Work extraction from unknown quantum sources
• Detecting entanglement in quantum many-body systems via permutation moments
• Classical shadows with Pauli-invariant unitary ensembles
• Multivariate trace estimation in constant quantum depth
• One-axis twisting as a method of generating many-body Bell correlations
• Performance analysis of multi-shot shadow estimation
• Direct measurement of quantum Fisher information
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator
• Experimental demonstration of topological bounds in quantum metrology
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
• Uncertainty Relation for Non-Hermitian Systems
• Fermionic correlation functions from randomized measurements in programmable atomic quantum devices
• Entanglement phase diagrams from partial transpose moments
• Evaluating the quantum Ziv-Zakai bound in noisy environments
• Method for Generating Randomly Perturbed Density Operators Subject to Different Sets of Constraints
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming