Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness

Abstract

Estimating the quantum Fisher information (QFI) is a crucial yet challenging task with widespread applications across quantum science and technologies. The recently proposed Krylov shadow tomography (KST) opens a new avenue for this task by introducing a series of Krylov bounds on the QFI. In this work, we address the practical applicability of the KST, unveiling that the Krylov bounds of low orders already enable efficient and accurate estimation of the QFI. We show that the Krylov bounds converge to the QFI exponentially fast with increasing order and can surpass the state-of-the-art polynomial lower bounds known to date. Moreover, we show that certain low-order Krylov bound can already match the QFI exactly for low-rank states prevalent in practical settings. Such exact match is beyond the reach of polynomial lower bounds proposed previously. These theoretical findings, solidified by extensive numerical simulations, demonstrate practical advantages over existing polynomial approaches, holding promise for fully unlocking the effectiveness of QFI-based applications.

Published version, 9+4pages, 6 figures

References in corpus (29)

• Entanglement detection
• Quantum metrology from a quantum information science perspective
• Quantum critical scaling of the geometric tensors
• The randomized measurement toolbox
• Geometric phases and criticality in spin chain systems
• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification
• An operational interpretation for multipartite entanglement
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Metrological Detection of Multipartite Entanglement from Young Diagrams
• Entanglement barrier and its symmetry resolution: theory and experiment
• Non-Hermitian Floquet Topological Matter -- A Review
• Quantum Error Mitigated Classical Shadows
• Low-temperature quantum thermometry boosted by coherence generation
• Probe optimization for quantum metrology via closed-loop learning control
• Approaching Heisenberg-scalable thermometry with built-in robustness against noise
• Robust estimation of the Quantum Fisher Information on a quantum processor
• Sub-Quantum Fisher Information
• Quantum-enhanced metrology with network states
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Readout error mitigated quantum state tomography tested on superconducting qubits
• Strict hierarchy of optimal strategies for global estimations: Linking global estimations with local ones
• Inferring physical properties of symmetric states from the fewest copies
• Krylov shadow tomography: Efficient estimation of quantum Fisher information
• Universal freezing of asymmetry
• Retrieving maximum information of symmetric states from their corrupted copies
• Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms