Quantum multi-anomaly detection

Santiago Llorens; Gael Sentís; Ramon Muñoz-Tapia

doi:10.22331/q-2024-08-28-1452

Quantum multi-anomaly detection

Santiago Llorens¹, Gael Sentís^1,2, and Ramon Muñoz-Tapia¹

¹Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
²Ideaded, Carrer de la Tecnologia, 35, 08840 Viladecans, Barcelona, Spain

Published:	2024-08-28, volume 8, page 1452
Eprint:	arXiv:2312.13020v2
Doi:	https://doi.org/10.22331/q-2024-08-28-1452
Citation:	Quantum 8, 1452 (2024).

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Abstract

A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of $n$ preparations with $k$ anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large $n$ and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.

Featured image: Jonhson graph $J(5,2)$ for a set of $n=5$ objects with subsets of cardinality $k=2$. The graph's vertices correspond to the hypotheses to discriminate in a production of $n=5$ quantum states containing $k=2$ anomalies.

► BibTeX data

@article{Llorens2024quantummultianomaly,
  doi = {10.22331/q-2024-08-28-1452},
  url = {https://doi.org/10.22331/q-2024-08-28-1452},
  title = {Quantum multi-anomaly detection},
  author = {Llorens, Santiago and Sent{\'{i}}s, Gael and Mu{\~{n}}oz-Tapia, Ramon},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1452},
  month = aug,
  year = {2024}
}

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Cited by

[1] Michalis Skotiniotis, Santiago Llorens, Ronja Hotz, John Calsamiglia, and Ramon Muñoz-Tapia, "Identification of malfunctioning quantum devices", Physical Review Research 6 3, 033329 (2024).

[2] A. Diebra, S. Llorens, E. Bagan, G. Sentís, and R. Muñoz-Tapia, "Quantum state exclusion for group-generated ensembles of pure states", Physical Review Research 8 1, L012001 (2026).

[3] Caleb McIrvin, Ankith Mohan, and Jamie Sikora, "Quantum state exclusion through offset measurement", Physical Review A 110 4, 042211 (2024).

[4] Jeongho Bang, Wooyeong Song, Kyujin Shin, and Yong-Su Kim, "Ensuring superior learning outcomes and data security for authorized learner", Quantum Science and Technology 10 2, 025056 (2025).

[5] T. Crosta, L. Rebón, F. Vilariño, J. M. Matera, and M. Bilkis, "Automatic re-calibration of quantum devices by reinforcement learning", arXiv:2404.10726, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-12 21:34:58) and SAO/NASA ADS (last updated successfully 2026-08-12 21:34:59). The list may be incomplete as not all publishers provide suitable and complete citation data.

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