Krylov Distribution and Universal Convergence of Quantum Fisher Information

• URL: http://arxiv.org/abs/2602.19750v1
• Date: Mon, 23 Feb 2026 11:59:29 GMT
• Title: Krylov Distribution and Universal Convergence of Quantum Fisher Information
• Authors: Mohsen Alishahiha, Fatemeh Tarighi Tabesh, Mohammad Javad Vasli,
• Abstract summary: We develop a framework for computing the quantum Fisher information computation (QFI) using Krylov subspace methods.<n>By expressing the QFI as a resolvent moment of the superoperator $mathcalK_ universality associated with a density matrix, the Krylov distribution quantifies how the QFI weight is distributed across Krylov levels.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We develop a spectral-resolvent framework for computing the quantum Fisher information (QFI) using Krylov subspace methods, extending the notion of the Krylov distribution. By expressing the QFI as a resolvent moment of the superoperator $\mathcal{K}_ρ$ associated with a density matrix, the Krylov distribution quantifies how the QFI weight is distributed across Krylov levels in operator space and provides a natural measure for controlling the truncation error in Krylov approximations. Leveraging orthogonal polynomial theory, we identify two universal convergence regimes: exponential decay when the Liouville-space spectrum is gapped away from zero, and algebraic decay governed by hard-edge (Bessel) universality when small eigenvalues accumulate near zero. This framework establishes a direct connection between quantum metrology, spectral geometry, and Krylov dynamics, offering both conceptual insight and practical tools for efficient QFI computation in high-dimensional and many-body systems.

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