Pauli Error Composition Determines the Multipartite Advantage in Conference Key Agreement
Abstract
GHZ-based conference key agreement distributes a shared key to N parties in one network use, whereas pairwise BB84 needs N−1. The survival of that advantage has been studied against party number, loss, and topology, but almost always with the channel fixed at depolarizing. Simulating both protocols exactly for N = 3, 4, 5 under dephasing, amplitude damping, and depolarizing noise, we find the crossover is set by the channel's Pauli error composition, not its identity: normalized to average infidelity, amplitude damping and depolarizing agree to within about 1\% at each group size, while dephasing can tolerate roughly 2.4× more at N = 3. We derive a closed-form rate for arbitrary per-party Pauli noise and use it to prove that concentrating a fixed noise budget on one arm is strictly worse than spreading it, and that giving the dealer role to the cleanest arm improves the rate by roughly 18\%. One structural fact drives every result: the phase-error term is a product over all N arms, while the bit-error term stays local to a pair.
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BibTeX
@misc{carlson2026pauli,
title = {{Pauli Error Composition Determines the Multipartite Advantage in Conference Key Agreement}},
author = {Ryder Carlson and Lochlan Fitzgerald and Kidus Peter and Wilson Smith},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07251},
eprint = {2610.07251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07251},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Pauli Error Composition Determines the Multipartite Advantage in Conference Key Agreement
AU - Ryder Carlson
AU - Lochlan Fitzgerald
AU - Kidus Peter
AU - Wilson Smith
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07251
UR - https://arxiv.org/abs/2610.07251
AB - GHZ-based conference key agreement distributes a shared key to N parties in one network use, whereas pairwise BB84 needs N−1. The survival of that advantage has been studied against party number, loss, and topology, but almost always with the channel fixed at depolarizing. Simulating both protocols exactly for N = 3, 4, 5 under dephasing, amplitude damping, and depolarizing noise, we find the crossover is set by the channel's Pauli error composition, not its identity: normalized to average infidelity, amplitude damping and depolarizing agree to within about 1\% at each group size, while dephasing can tolerate roughly 2.4× more at N = 3. We derive a closed-form rate for arbitrary per-party Pauli noise and use it to prove that concentrating a fixed noise budget on one arm is strictly worse than spreading it, and that giving the dealer role to the cleanest arm improves the rate by roughly 18\%. One structural fact drives every result: the phase-error term is a product over all N arms, while the bit-error term stays local to a pair.
ER -