Cyclic measurements and simplified quantum state tomography

Victor Gonzalez Avella; Jakub Czartowski; Dardo Goyeneche; Karol Życzkowski

doi:10.22331/q-2025-06-04-1763

Cyclic measurements and simplified quantum state tomography

Victor Gonzalez Avella¹, Jakub Czartowski^2,3,4, Dardo Goyeneche^1,5, and Karol Życzkowski^3,6

¹Departamento de Física, Facultad de Ciencias Básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile
²Doctoral School of Exact and Natural Sciences, Jagiellonian University, ul. Lojasiewicza 11, 30-348 Kraków, Poland
³Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
⁴School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore
⁵Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
⁶Center for Theoretical Physics, Polish Academy of Sciences, ul Lotników 32/46, 02-668 Warszawa, Poland

Published:	2025-06-04, volume 9, page 1763
Editor:	Daniel McNulty
Eprint:	arXiv:2404.18847v4
Doi:	https://doi.org/10.22331/q-2025-06-04-1763
Citation:	Quantum 9, 1763 (2025).

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Abstract

Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and accessing information encoded in quantum-mechanical systems. Among the informationally complete sets of quantum measurements, the tight ones provide a linear reconstruction formula and minimize the propagation of statistical errors. However, implementing tight measurements in the lab is challenging due to the high number of required measurement projections, involving a series of experimental setup preparations. In this work, we introduce the notion of cyclic tight measurements, which allow us to perform full quantum state tomography while considering only repeated application of a single unitary-based quantum device during the measurement stage. This type of measurement significantly simplifies the complexity of the experimental setup required to retrieve the quantum state of a physical system. Additionally, we design a feasible setup preparation procedure that produces well-approximated cyclic tight measurements in every finite dimension.

► BibTeX data

@article{GonzalezAvella2025cyclicmeasurements,
  doi = {10.22331/q-2025-06-04-1763},
  url = {https://doi.org/10.22331/q-2025-06-04-1763},
  title = {Cyclic measurements and simplified quantum state tomography},
  author = {Gonzalez Avella, Victor and Czartowski, Jakub and Goyeneche, Dardo and {\.{Z}}yczkowski, Karol},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1763},
  month = jun,
  year = {2025}
}

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[1] Daniel McNulty and Stefan Weigert, "Mutually Unbiased Bases in Composite Dimensions – A Review", Quantum 10, 2051 (2026).

[2] Yunting Li and Huangjun Zhu, "Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases", Quantum 10, 2011 (2026).

[3] Joseph T. Iosue, T. C. Mooney, Adam Ehrenberg, and Alexey V. Gorshkov, "Projective toric designs, quantum state designs, and mutually unbiased bases", Quantum 8, 1546 (2024).

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