非厄米前馈链在局域驱动下的费舍尔信息保留
Fisher-information retention under local driving in non-Hermitian feed-forward chains
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中文总结 AI 辅助
该研究量化非厄米前馈链局域驱动下目标制备与空间覆盖的权衡，推导费舍尔信息保留定律，为端口布局提供准则，揭示定向性带来的源节省与未知任务覆盖成本的平衡关系。
中文摘要 AI 辅助
当局域驱动硬件在传感任务被明确前已安装时，定向非厄米积累会在目标制备与空间覆盖间形成权衡。我们针对具有恰当复高斯输出统计的稳定线性散射体量化该权衡：对于编码在内部生成器中的参数，在固定相干内部资源下，驱动硬件仅通过内部可达子空间上的投影器进入优化后的平均响应费舍尔信息，而制备格拉姆矩阵则设定源成本。在谐振前馈链中，嵌套格林函数列可分解为不相交的端口区间，每个区间内的位点局域保留因子之和恰好为1。定向性将该单位集中到下游，因此当一个端口服务多个位点时，最差位点的保留因子呈指数衰减；对于m个相等区间，所有任务共享单个探针的最差位点保留因子，比任务特定重新优化的结果低m倍。源功率与内部资源的联合约束将该固定资源定律与源受限制备关联起来。含噪声RLC/VCCS模型通过存储的电磁能量、协方差费舍尔信息及组件无序性阐释了保留定律。所得边界将定向积累转化为端口布局准则：选定任务的源节省，伴随着硬件设计阶段未知任务的空间覆盖成本。
英文摘要
When local drive hardware is installed before a sensing task is revealed, directional non-Hermitian buildup creates a tradeoff between targeted preparation and spatial coverage. We quantify this tradeoff for stable linear scatterers with proper complex Gaussian output statistics. For parameters encoded in the internal generator, and at fixed coherent internal resource, the drive hardware enters the optimized mean-response Fisher information only through the projector onto the internally reachable subspace, while the preparation Gramian sets the source cost. In an on-resonance feed-forward chain, nested Green-function columns decompose into disjoint port intervals, and the site-local retention factors in each interval sum exactly to unity. Directionality concentrates this unit downstream, so the worst-site retention decays exponentially when one port serves many sites; for $m$ equal intervals, a single probe shared by all tasks has a worst-site retention lower by a further factor $m$ than task-specific reoptimization. Joint source-power and internal-resource constraints connect this fixed-resource law to source-limited preparation. A noisy RLC/VCCS model illustrates the retention law with stored electromagnetic energy, covariance Fisher information, and component disorder. The resulting bounds turn directional buildup into a port-layout criterion: source savings for a selected task are accompanied by a spatial coverage cost for tasks unknown at the hardware-design stage.
发表机构
- School of Electronic Science and Engineering, Nanjing University（南京大学电子科学与工程学院）
- School of Integrated Circuits, Nanjing University（南京大学集成电路学院）
- National Key Laboratory of Transient Impact（瞬态冲击效应国家重点实验室）
- Key Laboratory of Intelligent Optical Sensing and Manipulation, Ministry of Education, Nanjing University（教育部智能光电感知与操纵重点实验室（南京大学））
- Jiangsu Key Laboratory of Semiconductor Laser and Sensing Technology（江苏省半导体激光与传感技术重点实验室）
- Wujin-NJU Institute of Future Technology（武进-南大未来技术研究院）
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