The minimal example of quantum network Bell nonlocality
Abstract
In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open question is to identify the minimal network configuration in which quantum resources produce Bell nonlocal correlations. Here we address this question and show that quantum nonlocality is possible in the triangle network where the parties have no input choices and produce only binary-valued outcomes. To do so, we start by identifying a family of target distributions and proving their nonlocality. Next, we construct an explicit quantum model that reproduces the target distributions to machine precision. For this, we develop an efficient method for parameterizing quantum distributions in networks, inspired by the formalism of higher-order quantum operations. When considering the number of observed variables and their cardinality, this constitutes the smallest scenario possible that supports quantum nonlocality in networks. Moreover, by analyzing the explicit quantum model, we obtain new insights into how nonlocal distributions can be generated in quantum networks.
Related
- Quantum entanglement and Bell nonlocality in top-quark pair production at a photon linear collider
- Quantum communication and Bell nonlocality require infinite classical communication to simulate
- All Bell inequalities with a quantum advantage in the minimal scenario are self-testing
- Exact Identification of Quantum Correlations in the Minimal Bell Scenario
- Bell nonlocality does not imply violation of nonlocal games
BibTeX
@misc{don2026minimal,
title = {{The minimal example of quantum network Bell nonlocality}},
author = {Erwan Don and Jessica Bavaresco and Patryk Lipka-Bartosik and Nicolas Gisin and Nicolas Brunner and Alejandro Pozas-Kerstjens},
howpublished = {HAL},
year = {2026},
month = oct,
eprint = {2605.00981},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05791919v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The minimal example of quantum network Bell nonlocality
AU - Erwan Don
AU - Jessica Bavaresco
AU - Patryk Lipka-Bartosik
AU - Nicolas Gisin
AU - Nicolas Brunner
AU - Alejandro Pozas-Kerstjens
PY - 2026
DA - 2026/10/11
PB - HAL
UR - https://hal.science/hal-05791919v1
AB - In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open question is to identify the minimal network configuration in which quantum resources produce Bell nonlocal correlations. Here we address this question and show that quantum nonlocality is possible in the triangle network where the parties have no input choices and produce only binary-valued outcomes. To do so, we start by identifying a family of target distributions and proving their nonlocality. Next, we construct an explicit quantum model that reproduces the target distributions to machine precision. For this, we develop an efficient method for parameterizing quantum distributions in networks, inspired by the formalism of higher-order quantum operations. When considering the number of observed variables and their cardinality, this constitutes the smallest scenario possible that supports quantum nonlocality in networks. Moreover, by analyzing the explicit quantum model, we obtain new insights into how nonlocal distributions can be generated in quantum networks.
ER -