Near-Optimal Bell Nonlocality with GKP and Entangled Cat States
Abstract
Gottesman-Kitaev-Preskill (GKP) states are widely studied as a bosonic encoding for fault-tolerant quantum computing because small displacement errors can be identified and corrected through syndrome measurements. However, fault-tolerant operation requires substantially greater GKP squeezing than is currently available in optical platforms. It is therefore important to identify quantum-information tasks that can be realised with finite-squeezing GKP states. Here, we study Bell nonlocality in finite-energy GKP Bell states under experimentally motivated measurement constraints. Although finite-energy GKP Bell states support Bell nonlocality even at low squeezing, logical Pauli measurements alone cannot reveal it. Accessing the maximum CHSH violation supported by the state generally requires logical non-Clifford rotations. We instead show that the required non-Gaussian resource can reside in the measurement itself. Photon-number-resolving detection combined with Gaussian preprocessing and adaptive feed-forward closely approaches the maximum violation of the CHSH Bell inequality without implementing logical non-Clifford gates. The same measurement principle strongly enhances Bell violations for cat-code Bell pairs and entangled coherent states, demonstrating that its usefulness extends beyond the GKP lattice. Our results identify non-Gaussian measurements as a practical route to revealing Bell nonlocality in finite-energy bosonic states.
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BibTeX
@misc{erkılıc2026nearoptimal,
title = {{Near-Optimal Bell Nonlocality with GKP and Entangled Cat States}},
author = {Özlem Erkılıç and Aritra Das and S. Nibedita Swain and Simon Devitt and Timothy C. Ralph},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27640},
eprint = {2609.27640},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27640},
}
RIS
TY - UNPB
TI - Near-Optimal Bell Nonlocality with GKP and Entangled Cat States
AU - Özlem Erkılıç
AU - Aritra Das
AU - S. Nibedita Swain
AU - Simon Devitt
AU - Timothy C. Ralph
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27640
UR - https://arxiv.org/abs/2609.27640
AB - Gottesman-Kitaev-Preskill (GKP) states are widely studied as a bosonic encoding for fault-tolerant quantum computing because small displacement errors can be identified and corrected through syndrome measurements. However, fault-tolerant operation requires substantially greater GKP squeezing than is currently available in optical platforms. It is therefore important to identify quantum-information tasks that can be realised with finite-squeezing GKP states. Here, we study Bell nonlocality in finite-energy GKP Bell states under experimentally motivated measurement constraints. Although finite-energy GKP Bell states support Bell nonlocality even at low squeezing, logical Pauli measurements alone cannot reveal it. Accessing the maximum CHSH violation supported by the state generally requires logical non-Clifford rotations. We instead show that the required non-Gaussian resource can reside in the measurement itself. Photon-number-resolving detection combined with Gaussian preprocessing and adaptive feed-forward closely approaches the maximum violation of the CHSH Bell inequality without implementing logical non-Clifford gates. The same measurement principle strongly enhances Bell violations for cat-code Bell pairs and entangled coherent states, demonstrating that its usefulness extends beyond the GKP lattice. Our results identify non-Gaussian measurements as a practical route to revealing Bell nonlocality in finite-energy bosonic states.
ER -