Certifying nonlocal properties of noisy quantum operations

Albert Rico; Moisés Bermejo Morán; Fereshte Shahbeigi; Karol Życzkowski

doi:10.22331/q-2025-07-22-1807

Certifying nonlocal properties of noisy quantum operations

Albert Rico¹, Moisés Bermejo Morán^1,2, Fereshte Shahbeigi^1,3, and Karol Życzkowski^1,4

¹Faculty of Physics, Astronomy and Applied Computer Science, Institute of Theoretical Physics, Jagiellonian University, 30-348 Kraków, Poland
²Laboratoire d’Information Quantique, Université libre de Bruxelles, Belgium
³RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia
⁴Center for Theoretical Physics, Polish Academy of Science, 02-668 Warszawa, Poland

Published:	2025-07-22, volume 9, page 1807
Editor:	Nicolai Friis
Eprint:	arXiv:2407.02570v3
Doi:	https://doi.org/10.22331/q-2025-07-22-1807
Citation:	Quantum 9, 1807 (2025).

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Abstract

Certifying quantum properties from the probability distributions they induce is an important task for several purposes. While this framework has been largely explored and used for quantum states, its extrapolation to the level of channels started recently in a variety of approaches. In particular, little is known about to what extent noise can spoil certification methods for channels. In this work we provide a unified methodology to certify nonlocal properties of quantum channels from the correlations obtained in prepare-and-measurement protocols: our approach gathers fully and semi-device-independent existing methods for this purpose, and extends them to new certification criteria. In addition, the effect of different models of dephasing noise is analysed. Some noise models are shown to generate nonlocality and entanglement in special cases. In the extreme case of complete dephasing, the measurement protocols discussed yield particularly simple tests to certify nonlocality, which can be obtained from known criteria by fixing the dephasing basis. These are based on the relations between bipartite quantum channels and their classical analogues: bipartite stochastic matrices defining conditional distributions.

Popular summary

Quantum operations determine the evolution of quantum systems. Operations acting on bipartite systems induce the nonlocal defining properties inherent to quantum mechanics. Therefore, it is crucial to understand the non-local features of quantum operations, which account for their nonlocal capabilities. Here we reveal such properties from the probability of detector clicks, conditional to input state preparations that can be determined by classical means like coin-tossing. We examine in detail the effects of noise in such detection methods, and find extremal phenomena in principle allowed by the most general theory of dephasing. Finally, we focus on the completely decoherent case, where only classical state preparations and measurements can effectively be done. In such case, states are mapped to probabilities and channels to conditional distributions. In this scenario, we still reveal the full structure of nonlocality in channels by local preparation-measurements in the computational basis.

► BibTeX data

@article{Rico2025certifyingnonlocal,
  doi = {10.22331/q-2025-07-22-1807},
  url = {https://doi.org/10.22331/q-2025-07-22-1807},
  title = {Certifying nonlocal properties of noisy quantum operations},
  author = {Rico, Albert and Mor{\'{a}}n, Mois{\'{e}}s Bermejo and Shahbeigi, Fereshte 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 = {1807},
  month = jul,
  year = {2025}
}

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Cited by

[1] Albert Rico, Moisés Bermejo Morán, Fereshte Shahbeigi, and Karol Życzkowski, "Channel Nonlocality under Decoherence", Physical Review Letters 136 11, 110202 (2026).

[2] Albert Rico, Moisés Bermejo Morán, Fereshte Shahbeigi, and Karol Życzkowski, "Channel nonlocality under decoherence", arXiv:2408.10317, (2024).

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