Krylov Distribution and Universal Convergence of Quantum Fisher Information
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914490761609216 |
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| author | Alishahiha, Mohsen Tabesh, Fatemeh Tarighi Vasli, Mohammad Javad |
| author_facet | Alishahiha, Mohsen Tabesh, Fatemeh Tarighi Vasli, Mohammad Javad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19750 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Krylov Distribution and Universal Convergence of Quantum Fisher Information Alishahiha, Mohsen Tabesh, Fatemeh Tarighi Vasli, Mohammad Javad Quantum Physics Statistical Mechanics High Energy Physics - Theory 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. |
| title | Krylov Distribution and Universal Convergence of Quantum Fisher Information |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.19750 |