Estimation of high-dimensional unitary transformations saturating the Quantum Cramér-Rao bound

J. Escandón-Monardes; D. Uzcátegui; M. Rivera-Tapia; S. P. Walborn; A. Delgado

doi:10.22331/q-2024-07-10-1405

Estimation of high-dimensional unitary transformations saturating the Quantum Cramér-Rao bound

J. Escandón-Monardes, D. Uzcátegui, M. Rivera-Tapia, S. P. Walborn, and A. Delgado

Departamento de Física, Universidad de Concepción, 160-C Concepción, Chile
Millennium Institute for Research in Optics, Universidad de Concepción, 160-C Concepción, Chile

Published:	2024-07-10, volume 8, page 1405
Eprint:	arXiv:2310.12699v2
Doi:	https://doi.org/10.22331/q-2024-07-10-1405
Citation:	Quantum 8, 1405 (2024).

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Abstract

We propose an estimation procedure for $d$-dimensional unitary transformations. For $d\gt2$, the unitary transformations close to the identity are estimated saturating the quantum Cramér-Rao bound. For $d=2$, the estimation of all unitary transformations is also optimal with some prior information. We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography.

Featured image: We estimate $2$-dimensional unitary transformations without prior information and compare with Standard Quantum Process Tomography (SQPT). We simulate both procedures on Qiskit and study the average gate fidelity as a function of the ensemble size, or number of shots, for a set of randomly generated unitary transformations. In the absence of error sources, our estimation procedure (solid green dots) achieves greater precision than SQPT (solid red dots).

► BibTeX data

@article{EscandonMonardes2024estimationofhigh,
  doi = {10.22331/q-2024-07-10-1405},
  url = {https://doi.org/10.22331/q-2024-07-10-1405},
  title = {Estimation of high-dimensional unitary transformations saturating the {Q}uantum {C}ram{\'{e}}r-{R}ao bound},
  author = {Escand{\'{o}}n-Monardes, J. and Uzc{\'{a}}tegui, D. and Rivera-Tapia, M. and Walborn, S. P. and Delgado, A.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1405},
  month = jul,
  year = {2024}
}

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Cited by

[1] Jorge Escandón-Monardes, Daniel Uzcátegui-Contreras, Marco Rivera-Tapia, Marcin Pawłowski, Łukasz Rudnicki, Aldo Delgado, and Stephen P. Walborn, "Transcribing quantum channels into quantum states", Physical Review A 112 5, 052429 (2025).

[2] Yannick Deville and Alain Deville, ICASSP 2026 - 2026 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 20407 (2026) ISBN:979-8-3315-6701-9.

[3] Yannick Deville and Alain Deville, "Multi-stage tomography based on eigenanalysis for high-dimensional dense unitary processes in gate-based quantum computers", Discover Quantum Science 2 1, 29 (2026).

[4] Salini Rajeev and Mayukh Lahiri, "Characterizing a high-dimensional unitary transformation without measuring the qudit it transforms", Optics Letters 51 4, 853 (2026).

[5] Simone Cavazzoni, Berihu Teklu, and Matteo G. A. Paris, "Frequency estimation by frequency jumps", npj Quantum Information 11 1, 174 (2025).

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