arXiv subjects

Xinqi Hu

Publications and source records attributed to Xinqi Hu.

3 recordsLinked to original sources

arXiv2026

Operational Thresholds for Long-Range Entanglement in Quantum Networks

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, $η_p = 2 - \frac{32}{27}η_s$, 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 $S_\infty = 3/(4η_s)$. 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.

quant-ph↗

arXiv2025

Unveiling the Importance of Nonshortest Paths in Quantum Networks

Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. We apply a statistical physics model -- concurrence percolation -- to uncover the origin of stronger connectivity on hierarchical scale-free networks, the ($U,V$) flowers. These networks allow full analytical control over path connectivity through two adjustable path-length parameters, $U \leq V$. This precise control enables us to determine critical exponents well beyond current simulation limits, revealing that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from how they "superpose" parallel, non-shortest path contributions into overall connectivity. Concurrence percolation, unlike its classical counterpart, is sensitive to non-shortest paths and shows higher resilience to detours as these paths lengthen. This enhanced resilience is also observed in real-world hierarchical, scale-free Internet networks. Our findings highlight a crucial principle for QN design: when non-shortest paths are abundant, they notably enhance QN connectivity beyond what is achievable with classical percolation.

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arXiv2023

Percolation Theories for Quantum Networks

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called ``concurrence percolation,'' which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

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