Krylov shadow tomography: Efficient estimation of quantum Fisher information
arXiv:2503.01697 · doi:10.1103/PhysRevLett.134.110802
Abstract
Efficiently estimating the quantum Fisher information (QFI) is pivotal in quantum information science but remains an outstanding challenge for large systems due to its high nonlinearity. In this Letter, we tackle this long-standing challenge by integrating the Krylov subspace method--a celebrated tool from applied mathematics--into the framework of shadow tomography. The integrated technique, dubbed Krylov shadow tomography (KST), enables us to formulate a strict hierarchy of non-polynomial lower bounds on the QFI, among which the highest one matches the QFI exactly. We show that all the bounds can be expressed as expected values of the inverses of Hankel matrices, which are accessible via shadow tomography. Our KST therefore opens up a resource-efficient and experimentally feasible avenue to estimate not only non-polynomial lower bounds but also the QFI itself.
To be published in Phys. Rev. Lett
References in corpus (63)
- Quantum entanglement
- Quantum Computing in the NISQ era and beyond
- Quantum metrology
- Entanglement detection
- Quantum Coherence as a Resource
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Quantum state tomography via compressed sensing
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Quantum metrology from a quantum information science perspective
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Probing entanglement entropy via randomized measurements
- Fisher information and multiparticle entanglement
- Multipartite entanglement and high precision metrology
- Experimental EPR-Steering of Bell-local States
- Fisher Information and entanglement of non-Gaussian spin states
- Quantum Metrology for Gravitational Wave Astronomy
- The randomized measurement toolbox
- A Universal Operator Growth Hypothesis
- Measuring multipartite entanglement via dynamic susceptibilities
- Mixed-state entanglement from local randomized measurements
- Quantum coherence and geometric quantum discord
- Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
- Experimental Detection of Entanglement with Polarized Photons
- Sample-optimal tomography of quantum states
- Cross-Platform Verification of Intermediate Scale Quantum Devices
- Learning Quantum Systems
- 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
- Detecting large quantum Fisher information with finite measurement precision
- Fisher Information in Noisy Intermediate-Scale Quantum Applications
- Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
- Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
- An operational interpretation for multipartite entanglement
- Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox
- Metrological Detection of Multipartite Entanglement from Young Diagrams
- Optimal Entanglement Certification from Moments of the Partial Transpose
- Quantum Fisher information measurement and verification of the quantum Cramér-Rao bound in a solid-state qubit
- Quantum states with a positive partial transpose are useful for metrology
- Detecting metrologically useful asymmetry and entanglement by a few local measurements
- Realization of logically labeled effective pure states for bulk quantum computation
- Observing information backflow from controllable non-Markovian multi-channels in diamond
- Estimating coherence measures from limited experimental data available
- Shortcuts to Adiabaticity in Krylov Space
- Quantum metrology: Heisenberg limit with bound entanglement
- Quantum metrology beyond the Quantum Cramér-Rao theorem
- Detecting entanglement in quantum many-body systems via permutation moments
- Optimal witnessing of the quantum Fisher information with few measurements
- Activating hidden metrological usefulness
- Probe optimization for quantum metrology via closed-loop learning control
- Approaching Heisenberg-scalable thermometry with built-in robustness against noise
- Analysing quantum systems with randomised measurements
- Robust estimation of the Quantum Fisher Information on a quantum processor
- Sub-Quantum Fisher Information
- Quantum metrology in the noisy intermediate-scale quantum era
- Quantum-enhanced metrology with network states
- Experimental detection of entanglement with optimal-witness families
- Dissipative Adiabatic Measurements: Beating the Quantum Cramér-Rao Bound
- Bound entangled singlet-like states for quantum metrology
- Intrinsic metrological resolution as a distance measure and nonclassical light
- Strict hierarchy of optimal strategies for global estimations: Linking global estimations with local ones
- Inferring physical properties of symmetric states from the fewest copies
- Quantum delocalization on correlation landscape: The key to exponentially fast multipartite entanglement generation
- Metrological usefulness of entanglement and nonlinear Hamiltonians
Cited by in corpus (7)
- Generic Two-Mode Gaussian States as Quantum Sensors
- Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
- Quantum Fisher information from tensor network integration of Lyapunov equation
- Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
- Fundamental limits to contrast reversal of survival probability correlations
- Constrained Shadow Tomography for Molecular Simulation on Quantum Devices
- Scalable protocol to coherence estimation from scarce data: Theory and experiment