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  • Open Access

Optimal Overlapping Tomography

Kiara Hansenne1,2,*, Rui Qu3,4,†, Lisa T. Weinbrenner1, Carlos de Gois1, Haifei Wang3,4, Yang Ming3, Zhengning Yang3, Paweł Horodecki5,6, Weibo Gao3,4,‡ et al.

Otfried Gühne1,§

  • *Contact author: kiara.hansenne@ipht.fr
  • †Contact author: rui.qu@ntu.edu.sg
  • ‡Contact author: wbgao@ntu.edu.sg
  • §Contact author: otfried.guehne@uni-siegen.de
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Phys. Rev. Lett. 135, 060801 – Published 4 August, 2025

DOI: https://doi.org/10.1103/t6qb-kdcp

Abstract

Characterizing large-scale quantum systems is central to fundamental physics and essential for applications of quantum technologies. While a full characterization requires exponentially increasing resources, focusing on application-relevant information can often lead to significantly simplified analysis. Overlapping tomography is such a scheme, allowing one to obtain all the information contained in specific subsystems of multiparticle quantum systems in an efficient manner, but the ultimate limits of this approach remain elusive. We present protocols for overlapping tomography that are optimal with respect to the number of measurement settings. First, by providing algorithmic approaches based on graph theory we find the minimal number of Pauli settings, relating overlapping tomography to the problem of covering arrays in combinatorics. This significantly reduces the number of measurement settings, showing for instance that two-body overlapping tomography of nearest neighbors in qubit systems with planar topologies can always be performed with nine Pauli settings. Second, we prove that using general projective measurements, all k-body marginals can be reconstructed with only 3k settings, independently of the system size. Finally, we demonstrate the practical applicability of our methods in a six-photon experiment. Our results will find applications in learning noise and interaction patterns in quantum computers as well as characterizing fermionic systems in quantum chemistry.

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Phys. Rev. Lett. 135, 060801– Published 4 August, 2025
  • Received 23 December 2024
  • Revised 27 June 2025
  • Accepted 14 July 2025
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