信息的形态：多任务量子系统中的全局信息几何极限
The Shape of Information: Global Information Geometric Limits in Multi-task Quantum Systems
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中文总结 AI 辅助
该研究针对多任务量子系统，提出全局量子费舍尔信息矩阵（g-QFIM）作为多任务评估的统一信息几何约束，推导Holevo信息上界，揭示结构相变，经模拟验证，为量子多任务系统设计提供原理支撑。
中文摘要 AI 辅助
未来量子网络有望在单一系统内同时执行多项任务，例如集成感知与通信（ISAC）架构。尽管存在多种度量标准，我们发现多任务的评估可通过其信息容量实现统一，且总任务容量并非简单由加法决定，而是从根本上受限于一种我们称为全局量子费舍尔信息矩阵（g-QFIM）的信息几何。基于这一见解，我们推导了多任务系统Holevo信息的非渐近、与测量无关的上界，其形式类似香农容量，该上界不仅可量化容量极限，还可量化可分配性。我们的结果揭示了多任务性能在资源变化下的结构相变，即额外物理资源不再增加独立任务容量，而是将更多信息集中到新的单任务模式中。基于光子相位编码和实际噪声信道的数值模拟证实了这些预测。本研究为量子多任务系统建立了统一的信息几何原理，对未来量子网络和ISAC架构的设计具有重要意义。
英文摘要
Future quantum networks are expected to perform multiple tasks simultaneously within a single system, such as integrated sensing and communication (ISAC) architectures. Despite various metrics, we find that the evaluation of multiple tasks can be unified by their information capacity, and the total task capacity is not determined simply by addition, but is fundamentally constrained by an information geometry which we call the global quantum Fisher information matrix (g-QFIM). With this insight, we derive a non-asymptotic, measurement-independent upper bound on the Holevo information for multi-task systems, which takes a Shannon-capacity-like form. It not only quantifies the capacity limit, but also the allocability. Our results reveal a structural phase transition in multi-task performance under resource variation, where additional physical resources no longer increase independent task capacity but instead concentrate more information into a new mono-task mode. Numerical simulations based on photonic phase encoding and realistic noise channels confirm these predictions. This work establishes a unified information-geometric principle for quantum multi-task systems, with implications for the design of future quantum networks and ISAC architectures.
发表机构
- Peking University（北京大学）
- Beijing Institute of Technology（北京理工大学）
机构由 AI 辅助整理，请以论文原文为准。
