串联-并联量子网络中纠缠渗流的算子理论模型
An Operator-Theoretic Model of Entanglement Percolation in Series-Parallel Quantum Networks
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中文总结 AI 辅助
本文针对大规模量子网络中纠缠分发缺乏可解释性的问题，利用算子理论为串联-并联量子网络构建纠缠渗流的数学框架，并分析关键问题。
中文摘要 AI 辅助
在大规模量子网络（QNs）中实现纠缠分发（ED），作为量子通信的基本理论框架，面临着重大挑战。源自统计物理的渗流理论已被认为是解决该问题的潜在方案。然而，在处理ED时，渗流理论主要依赖于数值模拟和近似算法。这种方法对于大规模网络中ED过程中出现的许多现象（包括阈值附近的涌现现象）往往缺乏可解释性和可控性。为解决这些局限性，本文聚焦于利用算子理论为串联-并联QNs中的纠缠渗流构建一个数学框架。通过应用算子理论方法，我们分析了纠缠渗流过程中的几个关键问题。
英文摘要
The realization of entanglement distribution (ED) in large-scale quantum networks (QNs), as a fundamental theoretical framework of quantum communication, faces significant challenges. Percolation theory, drawn from statistical physics, has been identified as a potential solution to this problem. Nevertheless, when addressing ED, percolation theory primarily relies on numerical simulations and approximate algorithms. This approach often lacks interpretability and controllability for many phenomena occurring during the ED process in large-scale networks, including emergent phenomena near the threshold. To address these limitations, in this paper, we {focus on} leveraging operator theory to construct a mathematical framework for entanglement percolation in series-parallel QNs. Through the application of operator-theoretic methodologies, we analyze several critical issues within the entanglement percolation process.
发表机构
- College of Mathematics, Taiyuan University of Technology（太原理工大学数学学院）
- School of Mathematics and Statistics, Shaanxi Normal University（陕西师范大学数学与统计学院）
- School of Mathematics, Xi’an University of Technology（西安理工大学数学学院）
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