Memory attacks in network nonlocality and self-testing

Mirjam Weilenmann; Costantino Budroni; Miguel Navascues

doi:10.22331/q-2025-05-06-1735

Memory attacks in network nonlocality and self-testing

Mirjam Weilenmann¹, Costantino Budroni², and Miguel Navascues³

¹Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris, 91120 Palaiseau, France
²Department of Physics ``E. Fermi'' University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
³Institute for Quantum Optics and Quantum Information–IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria

Published:	2025-05-06, volume 9, page 1735
Editor:	Laura Mančinska
Eprint:	arXiv:2402.12318v2
Doi:	https://doi.org/10.22331/q-2025-05-06-1735
Citation:	Quantum 9, 1735 (2025).

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Abstract

We study what can or cannot be certified in communication scenarios where the assumption of independence and identical distribution (iid) between experimental rounds fails. In this respect, we prove that membership tests for non-convex sets of correlations cannot be formulated in the non-iid regime. Similarly, it is impossible to self-test non-extreme quantum operations, such as mixed states, or noisy quantum measurements, unless one allows more than a single use thereof within the same experimental round. One consequence of our results is that non-classicality in causal networks without inputs cannot be experimentally demonstrated. By analyzing optimal non-iid strategies in the triangle scenario, we raise the need to take into account the prior communication required to set up a causal network.

Popular summary

Certifying properties of quantum systems demands rigorous statistical analysis of experimental data. This analysis typically employs hypothesis testing frameworks, for which researchers have developed various sophisticated statistical tools. Bell inequality experiments exemplify this approach — to conclusively rule out local hidden variable models without loopholes, scientists must adopt an adversarial perspective. This adversarial framing ensures the security of protocols built upon such experiments, including device-independent quantum key distribution.
The "memory loophole" represents a particular vulnerability where adversaries could potentially exploit information from previous experimental rounds to adjust the behavior of the measurement devices in subsequent ones and thus mimic the behavior of entangled particles. This vulnerability means that experimental rounds cannot be treated as independent and identically distributed (iid). While addressing this loophole has become standard practice in Bell experiments, similar precautions remain uncommon in other quantum information protocols, such as non-classicality tests for quantum networks and self-testing protocols not based on Bell nonlocality.
Our research examines the limitations on certification in communication scenarios when the iid assumption is abandoned. We focus on two fundamental certification tasks: (a) Demonstrating that experimental devices can generate measurement statistics outside a specified set of correlations, (b) Proving that experimental devices produce statistics close to a target distribution.
For the first task, we demonstrate that membership tests for non-convex sets of correlations become impossible in the non-iid regime. This finding has significant implications for causal networks where such non-convex correlation sets naturally emerge, as in the triangle scenario. Consequently, demonstrating non-classicality in input-free causal networks becomes experimentally impossible. For the second task, we establish that robust self-testing in non-iid scenarios is only feasible when the target distribution constitutes an extreme point of the set of physically possible correlations. This implies that self-testing mixed quantum states or non-extreme quantum measurements becomes impossible, regardless of the communication scenario, unless multiple identical preparations or measurements occur within a single experimental round.
Finally, we analyze non-iid strategies that separate participants arranged in a network might employ to pass non-classicality tests designed for iid scenarios. We observe that many such strategies, while technically compatible with the network configuration, would require violating the network's causal constraints during setup. This raises important questions about how prior communication might undermine the conclusions drawn from causal experiments.

► BibTeX data

@article{Weilenmann2025memoryattacksin,
  doi = {10.22331/q-2025-05-06-1735},
  url = {https://doi.org/10.22331/q-2025-05-06-1735},
  title = {Memory attacks in network nonlocality and self-testing},
  author = {Weilenmann, Mirjam and Budroni, Costantino and Navascues, Miguel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1735},
  month = may,
  year = {2025}
}

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Cited by

[1] Tamás Kriváchy and Martin Kerschbaumer, "Closing the Detection Loophole in the Triangle Network with High-Dimensional Photonic States", Physical Review Letters 135 16, 160803 (2025).

[2] Dhruv Baheti and Shubhayan Sarkar, "Topologically noise-robust network steering without inputs", Physical Review A 113 1, 012607 (2026).

[3] Salome Hayes-Shuptar, Daniel Bhatti, Ana Belen Sainz, and David Elkouss, "Linear Program Witness for Network Nonlocality in Arbitrary Networks", IEEE Journal on Selected Areas in Communications 44, 4585 (2026).

[4] Gábor Drótos, Károly F. Pál, and Tamás Vértesi, "Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario", Physical Review A 110 3, 032427 (2024).

[5] Víctor Calleja Rodríguez, Ivan A. Bocanegra-Garay, and Mateus Araújo, "Post-selection games", arXiv:2601.18861, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-10 13:05:18) and SAO/NASA ADS (last updated successfully 2026-08-10 13:05:19). The list may be incomplete as not all publishers provide suitable and complete citation data.

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