Noise-robust proofs of quantum network nonlocality
Department of Applied Physics, University of Geneva, Switzerland
| Published: | 2025-08-27, volume 9, page 1830 |
| Editor: | Maximilian Lock |
| Eprint: | arXiv:2311.02182v3 |
| Doi: | https://doi.org/10.22331/q-2025-08-27-1830 |
| Citation: | Quantum 9, 1830 (2025). |
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Abstract
Quantum networks allow for novel forms of quantum nonlocality. By exploiting the combination of entangled states and entangled measurements, strong nonlocal correlations can be generated across the entire network. So far, all proofs of this effect are essentially restricted to the idealized case of pure entangled states and projective local measurements. Here we present noise-robust proofs of network quantum nonlocality, for a class of quantum distributions on the triangle network that are based on entangled states and entangled measurements. The key ingredient is a result of approximate rigidity for local distributions that satisfy the so-called “parity token counting'' property with high probability. Our methods can be applied to any type of noise. As illustrative examples, we consider quantum distributions obtained with imperfect sources and obtain a noise robustness up to $\sim 80\%$ for dephasing noise and up to $\sim 0.5\%$ for white noise. Additionally, we prove that all distributions in the vicinity of some ideal quantum distribution are nonlocal, with a bound on the total-variation distance $\sim 0.25\%$. Our work opens interesting perspectives towards the practical implementation of quantum network nonlocality.
Popular summary
Establishing such robust network nonlocality is difficult: in principle one must exclude all classical (local) models compatible with the network structure, a vast and poorly tractable family. Our work overcomes this barrier via an "approximate rigidity" theorem tailored to the triangle. We identify a simple parity test — whether the three binary outcomes sum to an odd (or even) value with high probability — that tightly constrains any classical explanation. Specifically, we prove that observing this parity pattern forces every admissible classical model to be close to a parity–token-counting (PTC) strategy, a highly structured subclass that we can then rule out explicitly.
This reduction turns an intractable search over all classical models into a focused analysis of almost-PTC models. By excluding these, we certify nonlocality in the triangle under noisy conditions. With this in hand we present a family of quantum correlations that remain nonlocal when generic noise is introduced: dephasing, white noise, or bounded total variation distance to the ideal distribution.
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