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Peer-reviewedCC BY 4.0The European Physical Journal C

Krylov distribution and spectral convergence of quantum fisher information

  • M. Alishahiha1
  • F. T. Tabesh1
  • M. J. Vasli1
  1. 1Institute for Research in Fundamental Sciences (IPM)
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Abstract

We establish a direct correspondence between the Krylov hierarchy of quantum Fisher information (QFI) and a Krylov-resolved decomposition of the symmetric logarithmic derivative (SLD). Building on the existing Krylov formulation of QFI, we show that the metrological information resolved at each Krylov level is exactly encoded in the incremental gain of the Lanczos hierarchy, giving the Krylov distribution a direct information-theoretic interpretation. A dual spectral formulation distinguishes the Hilbert–Schmidt geometry used to construct the computational Lanczos hierarchy from the state-dependent geometry in which the SLD and QFI are naturally defined, and relates their associated Liouville measures. This distinction clarifies the origin of different convergence regimes: we recover exponential convergence for gapped spectra and derive an exact algebraic hard-edge convergence law for the Jacobi class, including the exact finite-order error and the marginal case separating finite from divergent QFI.

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Cite

BibTeXRIS
BibTeX
@article{alishahiha2026krylov,
  title = {{Krylov distribution and spectral convergence of quantum fisher information}},
  author = {M. Alishahiha and F. T. Tabesh and M. J. Vasli},
  journal = {The European Physical Journal C},
  year = {2026},
  month = oct,
  doi = {10.1140/epjc/s10052-026-16434-0},
  url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16434-0},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Krylov distribution and spectral convergence of quantum fisher information
AU  - M. Alishahiha
AU  - F. T. Tabesh
AU  - M. J. Vasli
PY  - 2026
DA  - 2026/10/19
JO  - The European Physical Journal C
DO  - 10.1140/epjc/s10052-026-16434-0
UR  - https://link.springer.com/article/10.1140/epjc/s10052-026-16434-0
AB  - We establish a direct correspondence between the Krylov hierarchy of quantum Fisher information (QFI) and a Krylov-resolved decomposition of the symmetric logarithmic derivative (SLD). Building on the existing Krylov formulation of QFI, we show that the metrological information resolved at each Krylov level is exactly encoded in the incremental gain of the Lanczos hierarchy, giving the Krylov distribution a direct information-theoretic interpretation. A dual spectral formulation distinguishes the Hilbert–Schmidt geometry used to construct the computational Lanczos hierarchy from the state-dependent geometry in which the SLD and QFI are naturally defined, and relates their associated Liouville measures. This distinction clarifies the origin of different convergence regimes: we recover exponential convergence for gapped spectra and derive an exact algebraic hard-edge convergence law for the Jacobi class, including the exact finite-order error and the marginal case separating finite from divergent QFI.
SN  - 1434-6044
SN  - 1434-6052
ER  -