Improving the Loss Tolerance of Heralded Photonic GHZ States for Long-Distance Device-Independent Conference Key Agreement
Abstract
Heralded multipartite entanglement distribution is a key requirement for device-independent conference key agreement (DI-CKA) over lossy quantum networks. Although locally equivalent in the absence of loss, different single-rail photon-number encodings of Greenberger--Horne--Zeilinger (GHZ) states respond differently to photon loss. Here, we investigate the critical detection efficiencies for detection-loophole-free parity--CHSH violations of computational-basis GHZ states---a coherent superposition of the vacuum and an n-photon component---and of fixed-photon-number GHZ states, deriving exact analytical conditions for both. We show that for states that are not permutation symmetric, such as the latter, the assignment of measurement roles to physical modes affects loss tolerance. We introduce a star-network protocol employing heterogeneous sources to directly herald the loss-tolerant vacuum-n-photon GHZ states while retaining the favourable long-distance scaling O(ηcn/2), where ηc is the channel transmittance. For four users, we characterize the heralded state under photon loss and show that tunable source parameters allow genuine multipartite entanglement to persist at any finite channel distance. With ideal Pauli and displacement-based measurements, our protocol achieves positive DI-CKA key rates at lower detection efficiencies than previous schemes, while retaining comparable or greater rates and communication distances at high efficiency. Overall, our work improves the loss tolerance of heralded photonic GHZ states for DI-CKA both by directly heralding a more loss-tolerant encoding and by optimizing existing schemes. These results identify photon-number encoding, source architecture, and measurement-role assignment as key design parameters for loss-resilient multipartite quantum networks, offering a practical route toward near-term DI-CKA.
Related
- Enhancing noise robustness in device-independent conference key agreement with asymmetric parity-CHSH inequalities
- Device-independent conference key agreement from two-body correlators with balanced Dicke states
- Pauli Error Composition Determines the Multipartite Advantage in Conference Key Agreement
- Performance Analysis of Multiparty GHZ-State Quantum Conference Key Agreement over Optical Fiber Channel
- Device-Independent Conference Keys from Parity-Extended Games
BibTeX
@misc{alwehaibi2026improving,
title = {{Improving the Loss Tolerance of Heralded Photonic GHZ States for Long-Distance Device-Independent Conference Key Agreement}},
author = {Yazeed K. Alwehaibi and Makoto Ishihara and Shakib Daryanoosh and Ewan Mer and Shang Yu and Wojciech Roga and Ian A. Walmsley and Masahiro Takeoka and Raj B. Patel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24941},
eprint = {2609.24941},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24941},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Improving the Loss Tolerance of Heralded Photonic GHZ States for Long-Distance Device-Independent Conference Key Agreement
AU - Yazeed K. Alwehaibi
AU - Makoto Ishihara
AU - Shakib Daryanoosh
AU - Ewan Mer
AU - Shang Yu
AU - Wojciech Roga
AU - Ian A. Walmsley
AU - Masahiro Takeoka
AU - Raj B. Patel
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.24941
UR - https://arxiv.org/abs/2609.24941
AB - Heralded multipartite entanglement distribution is a key requirement for device-independent conference key agreement (DI-CKA) over lossy quantum networks. Although locally equivalent in the absence of loss, different single-rail photon-number encodings of Greenberger--Horne--Zeilinger (GHZ) states respond differently to photon loss. Here, we investigate the critical detection efficiencies for detection-loophole-free parity--CHSH violations of computational-basis GHZ states---a coherent superposition of the vacuum and an n-photon component---and of fixed-photon-number GHZ states, deriving exact analytical conditions for both. We show that for states that are not permutation symmetric, such as the latter, the assignment of measurement roles to physical modes affects loss tolerance. We introduce a star-network protocol employing heterogeneous sources to directly herald the loss-tolerant vacuum-n-photon GHZ states while retaining the favourable long-distance scaling O(η_c^n/2), where η_c is the channel transmittance. For four users, we characterize the heralded state under photon loss and show that tunable source parameters allow genuine multipartite entanglement to persist at any finite channel distance. With ideal Pauli and displacement-based measurements, our protocol achieves positive DI-CKA key rates at lower detection efficiencies than previous schemes, while retaining comparable or greater rates and communication distances at high efficiency. Overall, our work improves the loss tolerance of heralded photonic GHZ states for DI-CKA both by directly heralding a more loss-tolerant encoding and by optimizing existing schemes. These results identify photon-number encoding, source architecture, and measurement-role assignment as key design parameters for loss-resilient multipartite quantum networks, offering a practical route toward near-term DI-CKA.
ER -