Multiparameter Maximum Information States for Coherent Diffraction Measurements

Abstract

In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the system is limited by photon noise. Here, we extend this approach to multiparameter estimation, in which case Fisher information takes the form of a matrix. We consider several scalar functions of the Fisher matrix to optimize the precision in multiple parameters at the same time. We also consider strategies for dealing with nuisance parameters, which can degrade the achievable precision of other parameters but are not of interest to measure. We corroborate our findings numerically using a scattering system of 2D coupled dipoles.

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BibTeX RIS

BibTeX

@misc{verreussel2026multiparameter,
  title = {{Multiparameter Maximum Information States for Coherent Diffraction Measurements}},
  author = {Bram Verreussel and Jacob Seifert and Allard Pieter Mosk},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.01445},
  eprint = {2606.01445},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.01445},
}

RIS

TY  - UNPB
TI  - Multiparameter Maximum Information States for Coherent Diffraction Measurements
AU  - Bram Verreussel
AU  - Jacob Seifert
AU  - Allard Pieter Mosk
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2606.01445
UR  - https://arxiv.org/abs/2606.01445
AB  - In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the system is limited by photon noise. Here, we extend this approach to multiparameter estimation, in which case Fisher information takes the form of a matrix. We consider several scalar functions of the Fisher matrix to optimize the precision in multiple parameters at the same time. We also consider strategies for dealing with nuisance parameters, which can degrade the achievable precision of other parameters but are not of interest to measure. We corroborate our findings numerically using a scattering system of 2D coupled dipoles.
ER  -

Abstract

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