Indefinite causal order strategy does not improve the estimation of group action

Masahito Hayashi

doi:10.22331/q-2025-10-22-1891

Indefinite causal order strategy does not improve the estimation of group action

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:	2025-10-22, volume 9, page 1891
Editor:	Philip Taranto
Eprint:	arXiv:2501.09312v2
Doi:	https://doi.org/10.22331/q-2025-10-22-1891
Citation:	Quantum 9, 1891 (2025).

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Abstract

We consider estimation of unknown unitary operation when the set of possible unitary operations is given by a projective unitary representation of a compact group. We show that neither indefinite causal order strategy nor adaptive strategy improves the performance of this estimation when error function satisfies group covariance. That is, the optimal parallel strategy gives the optimal performance even under indefinite causal order strategy and adaptive strategy. To study this problem, we newly introduce the concept of generalized positive operator valued measure (GPOVM), and its convariance condition. Using these concepts, we show the above statement.

► BibTeX data

@article{Hayashi2025indefinitecausal,
  doi = {10.22331/q-2025-10-22-1891},
  url = {https://doi.org/10.22331/q-2025-10-22-1891},
  title = {Indefinite causal order strategy does not improve the estimation of group action},
  author = {Hayashi, Masahito},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1891},
  month = oct,
  year = {2025}
}

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[1] Erik L André, Jessica Bavaresco, and Mohammad Mehboudi, "Strategy optimization for Bayesian quantum parameter estimation with finite copies: adaptive greedy, parallel, sequential, and general strategies", Quantum Science and Technology 11 3, 035040 (2026).

[2] Hongshun Yao and Xin Wang, "Conclusive exclusion of quantum states with group action", Physical Review A 113 2, 022205 (2026).

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

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

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