Heisenberg scaling based on population coding

Masahito Hayashi

doi:10.22331/q-2025-02-26-1648

Heisenberg scaling based on population coding

School of Data Science, The Chinese University of Hong Kong, Shenzhen, Longgang District, Shenzhen, 518172, China
International Quantum Academy, Futian District, Shenzhen 518048, China
Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan

Published:	2025-02-26, volume 9, page 1648
Editor:	Yu Tong
Eprint:	arXiv:2410.13399v2
Doi:	https://doi.org/10.22331/q-2025-02-26-1648
Citation:	Quantum 9, 1648 (2025).

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Abstract

We study Heisenberg scaling of quantum metrology in the viewpoint of population coding. Although Fisher information has been used for a figure of merit to characterize Heisenberg scaling in quantum metrology, several studies pointed out it does not work as a figure of merit because it does not reflect the global structure. As an alternative figure of merit, we propose the mutual information, which connects the number of distinguishable elements of the parameter space in the viewpoint of population coding. We show that several unitary models achieve Heisenberg scaling in this context.

► BibTeX data

@article{Hayashi2025heisenbergscaling,
  doi = {10.22331/q-2025-02-26-1648},
  url = {https://doi.org/10.22331/q-2025-02-26-1648},
  title = {Heisenberg scaling based on population coding},
  author = {Hayashi, Masahito},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1648},
  month = feb,
  year = {2025}
}

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Cited by

[1] Masahito Hayashi, Yu-Ao Chen, Chenghong Zhu, and Xin Wang, "Optimal sample complexity for testing unitary properties", Physical Review A 113 4, L040402 (2026).

[2] Masahito Hayashi, "Indefinite causal order strategy does not improve the estimation of group action", Quantum 9, 1891 (2025).

[3] Masahito Hayashi, "Indefinite causal order strategy does not improve the estimation of group action", arXiv:2501.09312, (2025).

[4] Masahito Hayashi, Yu-Ao Chen, Chenghong Zhu, and Xin Wang, "Predicting symmetries of quantum dynamics with optimal samples", arXiv:2502.01464, (2025).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 02:48:55) and SAO/NASA ADS (last updated successfully 2026-08-09 02:48:56). The list may be incomplete as not all publishers provide suitable and complete citation data.

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