Operational Thresholds for Long-Range Entanglement in Quantum Networks
Abstract
Quantum networks distribute entanglement between distant nodes by combining many short entangled links using local quantum operations. These operations only succeed probabilistically, yet existing percolation-based theories of entanglement transmission treat them as perfect. We approach the problem through statistical physics, using a stochastic generalization of concurrence percolation to determine how reliable local operations must be for long-range entanglement to remain possible. On hierarchical (U,V)-flower networks, which permit full analytical control across network scales, we derive an exact renormalization recursion for the probability that an end-to-end entangled connection survives. For the (2,2)-flower this yields a closed-form operational phase boundary, ηp = 2 − 32/27ηs, where ηs and ηp are the success probabilities of the series (entanglement swapping) and parallel (purification) operations, respectively. At this boundary the survival probability jumps discontinuously from $0$ to S∞ = 3/(4ηs). Numerically propagating the full distribution of end-to-end concurrence yields a second threshold in the initial link quality, which varies continuously with operational reliability. Above both thresholds the large-network state is binary: the connection either fails outright or approaches a perfect Bell pair. Our results thus reveal a two-threshold structure for long-range entanglement, in which operational reliability and initial link quality can compensate one another. Operational success rates therefore emerge alongside initial link quality as a primary design constraint for scalable quantum networks.
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BibTeX
@misc{caesar2026operational,
title = {{Operational Thresholds for Long-Range Entanglement in Quantum Networks}},
author = {Arn Caesar and Xinqi Hu and Kim Christensen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05069},
eprint = {2611.05069},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05069},
}
RIS
TY - UNPB
TI - Operational Thresholds for Long-Range Entanglement in Quantum Networks
AU - Arn Caesar
AU - Xinqi Hu
AU - Kim Christensen
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05069
UR - https://arxiv.org/abs/2611.05069
AB - Quantum networks distribute entanglement between distant nodes by combining many short entangled links using local quantum operations. These operations only succeed probabilistically, yet existing percolation-based theories of entanglement transmission treat them as perfect. We approach the problem through statistical physics, using a stochastic generalization of concurrence percolation to determine how reliable local operations must be for long-range entanglement to remain possible. On hierarchical (U,V)-flower networks, which permit full analytical control across network scales, we derive an exact renormalization recursion for the probability that an end-to-end entangled connection survives. For the (2,2)-flower this yields a closed-form operational phase boundary, η_p = 2 − 32/27η_s, where η_s and η_p are the success probabilities of the series (entanglement swapping) and parallel (purification) operations, respectively. At this boundary the survival probability jumps discontinuously from $0$ to S_∞ = 3/(4η_s). Numerically propagating the full distribution of end-to-end concurrence yields a second threshold in the initial link quality, which varies continuously with operational reliability. Above both thresholds the large-network state is binary: the connection either fails outright or approaches a perfect Bell pair. Our results thus reveal a two-threshold structure for long-range entanglement, in which operational reliability and initial link quality can compensate one another. Operational success rates therefore emerge alongside initial link quality as a primary design constraint for scalable quantum networks.
ER -