Joint-measurability and quantum communication with untrusted devices

Michele Masini; Marie Ioannou; Nicolas Brunner; Stefano Pironio; Pavel Sekatski

doi:10.22331/q-2024-12-23-1574

Joint-measurability and quantum communication with untrusted devices

Michele Masini¹, Marie Ioannou², Nicolas Brunner², Stefano Pironio¹, and Pavel Sekatski²

¹Laboratoire d'Information Quantique, Université libre de Bruxelles (ULB), Belgium
²Department of Applied Physics, University of Geneva, Switzerland

Published:	2024-12-23, volume 8, page 1574
Eprint:	arXiv:2403.14785v2
Doi:	https://doi.org/10.22331/q-2024-12-23-1574
Citation:	Quantum 8, 1574 (2024).

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Abstract

Photon loss represents a major challenge for the implementation of quantum communication protocols with untrusted devices, e.g. in the device-independent (DI) or semi-DI approaches. Determining critical loss thresholds is usually done in case-by-case studies. In the present work, we develop a general framework for characterizing the admissible levels of loss and noise in a wide range of scenarios and protocols with untrusted measurement devices. In particular, we present general bounds that apply to prepare-and-measure protocols for the semi-DI approach, as well as to Bell tests for DI protocols. A key step in our work is to establish a general connection between quantum protocols with untrusted measurement devices and the fundamental notions of channel extendibility and joint-measurability, which capture essential aspects of the communication and measurement of quantum information. In particular, this leads us to introduce the notion of partial joint-measurability, which naturally arises within quantum cryptography.

Featured image: A measurement unable to display "quantumness" can be implemented through a single quantum measurement $E_{\lambda}$. The classical output $\lambda$ is then transmitted and processed to generate the output $b$ depending on $y$.

Popular summary

Photon loss, which occurs during transmission or measurement of quantum states, is a critical problem in long-distance quantum communication. This issue becomes especially tricky in advanced quantum cryptography methods, such as device-independent and semi-device-independent protocols, where the devices are treated as potential black boxes that might not behave as expected.

We develop a general framework to determine how much loss and noise quantum communication setups can tolerate before losing their "quantumness"—essentially, the ability to exhibit quantum behaviors like entanglement or secure randomness. To do this, we make use of the concept of joint-measurability, which captures whether a set of quantum measurements can mimic classical ones. By connecting this concept to the security and performance of quantum protocols, the article lays out mathematical tools to assess when untrusted quantum devices become unreliable due to loss or noise. The work also presents a more flexible idea, partial joint-measurability, which is useful in scenarios where only some measurements are essential for tasks like generating secure cryptographic keys.

This research offers practical insights into how much loss or noise is acceptable in quantum communication setups, helping to design more robust protocols. It also deepens the understanding of quantum measurements, their compatibility, and how these factors influence the security of systems that rely on untrusted devices, with applications in quantum cryptography and beyond.

► BibTeX data

@article{Masini2024jointmeasurability,
  doi = {10.22331/q-2024-12-23-1574},
  url = {https://doi.org/10.22331/q-2024-12-23-1574},
  title = {Joint-measurability and quantum communication with untrusted devices},
  author = {Masini, Michele and Ioannou, Marie and Brunner, Nicolas and Pironio, Stefano and Sekatski, Pavel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1574},
  month = dec,
  year = {2024}
}

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Cited by

[1] Michele Masini and Shubhayan Sarkar, "One-sided DI-QKD secure against coherent attacks over long distances", New Journal of Physics 28 6, 064503 (2026).

[2] Sophie Egelhaaf, Jef Pauwels, Marco Túlio Quintino, and Roope Uola, "Certifying measurement incompatibility in prepare-and-measure and Bell scenarios", Journal of Physics A: Mathematical and Theoretical 58 9, 095304 (2025).

[3] Dmitry Grinko and Roope Uola, "Compatibility of Binary Qubit Measurements", Physical Review Letters 135 20, 200201 (2025).

[4] Tristan Le Roy-Deloison, Edwin Peter Lobo, Jef Pauwels, and Stefano Pironio, "Device-Independent Quantum Key Distribution Based on Routed Bell Tests", PRX Quantum 6 2, 020311 (2025).

[5] Nicolas Gigena, Ekta Panwar, Giovanni Scala, Mateus Araújo, Máté Farkas, and Anubhav Chaturvedi, "Self-testing tilted strategies for maximal loophole-free nonlocality", npj Quantum Information 11 1, 82 (2025).

[6] Edwin Peter Lobo, Jef Pauwels, and Stefano Pironio, "Certifying long-range quantum correlations through routed Bell tests", Quantum 8, 1332 (2024).

[7] Michele Masini and Shubhayan Sarkar, "One-sided DI-QKD secure against coherent attacks over long distances", arXiv:2403.11850, (2024).

[8] Edwin Peter Lobo, Maria Balanzó-Juandó, and Stefano Pironio, "Generalized measurement incompatibility", arXiv:2605.16151, (2026).

[9] Qiang Zeng, Abhishek Mishra, Haoyang Wang, and Zhiliang Yuan, "Transmitter-device-independent quantum key distribution", arXiv:2604.25225, (2026).

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