Interferometric binary phase estimations

Simone Roncallo; Xi Lu; Lorenzo Maccone

doi:10.22331/q-2025-04-18-1713

Interferometric binary phase estimations

Simone Roncallo^1,2, Xi Lu³, and Lorenzo Maccone^1,2

¹Dipartimento di Fisica, Università degli Studi di Pavia, Via Agostino Bassi 6, I-27100, Pavia, Italy
²INFN Sezione di Pavia, Via Agostino Bassi 6, I-27100, Pavia, Italy
³School of Mathematical Science, Zhejiang University, Hangzhou, 310027, China

Published:	2025-04-18, volume 9, page 1713
Editor:	Alioscia Hamma
Eprint:	arXiv:2407.10966v2
Doi:	https://doi.org/10.22331/q-2025-04-18-1713
Citation:	Quantum 9, 1713 (2025).

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Abstract

We propose an interferometric scheme where each photon returns one bit of the binary expansion of an unknown phase. It sets up a method for estimating the phase value at arbitrary uncertainty. This strategy is global, since it requires no prior information, and it achieves the Heisenberg bound independently of the output statistics. We provide simulations and a characterization of this architecture.

Featured image: Binary phase estimation. On the left, each line represents one photon going through the interferometer and providing a single bit of the binary expansion of the unknown phase. At the jth step, the output consists of a Fourier expansion of a square wave, with truncation order determined by the number D of subsequent applications of the interferometric module W. The true phase is sketched by the dashed vertical line. Combining all the outputs completes the estimation. The depth of the interferometer and the number of steps, i.e. the length of the binary expansion, determines the resource cost of the protocol. On the right, a comparison between the square wave and the optical response, obtained as the ratio of photons observed in the first mode for different choices of D.

Popular summary

In interferometry, we measure the length difference between two optical paths, encoded as an unknown phase transformation on a photon. In our manuscript, we present a novel phase estimation protocol, designed as a sequence of interferometric iterations, each providing one bit of the binary expansion of the unknown phase. We do this by designing an optical setup with a square wave response function, translating the estimation problem into a binary search task, and reconstructing the phase at arbitrary accuracy.

► BibTeX data

@article{Roncallo2025interferometric,
  doi = {10.22331/q-2025-04-18-1713},
  url = {https://doi.org/10.22331/q-2025-04-18-1713},
  title = {Interferometric binary phase estimations},
  author = {Roncallo, Simone and Lu, Xi and Maccone, Lorenzo},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1713},
  month = apr,
  year = {2025}
}

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Cited by

[1] Mateusz Duda, "A new binary-search approach to optical quantum metrology", Quantum Views 9, 86 (2025).

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Interferometric binary phase estimations

Abstract

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