AI 中文总结
研究多参量同时估计中，在多模高斯网络里给定压缩探测器时，有多少参数组合能继承海森堡标度。通过分析量子费希尔信息矩阵，得出海森堡标度系数秩的界限，确定饱和条件并构建干涉仪族。
AI 中文摘要
多参量同时估计是量子计量、分布式传感以及大型光子干涉仪校准中的核心任务。一个基本问题是在多模高斯网络中，从给定数量的压缩探测器中，有多少独立参数组合能继承海森堡标度。本文针对任意无源线性光学网络回答了这个问题。对于一个由\(k\)个单模压缩态探测且其余通道至少有一个相干态的\(p\)参数、\(M\)通道干涉仪，我们表明量子费希尔信息矩阵的海森堡标度系数的秩受限于\(n_{\rm HS}\le \min\{p,k(k + 3)/2\}\)，这对应于能以海森堡标度灵敏度估计的最大独立参数组合数。该界限分为两个几何上不同的贡献。量子费希尔信息的协方差贡献描述了压缩增强的涨落，最多提供\(k(k + 1)/2\)个能以海森堡标度灵敏度估计的参数组合，而一阶贡献最多提供\(k\)个额外的具有海森堡标度灵敏度的独立参数组合。我们确定了使这些界限饱和的条件，并构建了一个使这些界限饱和的无源干涉仪族。
英文摘要
The simultaneous estimation of multiple parameters is a central task in quantum metrology, distributed sensing, and the calibration of large photonic interferometers. A fundamental question is how many independent parameter combinations can inherit Heisenberg scaling from a given number of squeezed probes in a multimode Gaussian network. Here, we answer this question for arbitrary passive linear optical networks. For a $p$-parameter, $M$-channel interferometer probed by $k$ single-mode squeezed states and at least one coherent state in the remaining channels, we show that the rank of the Heisenberg-scaling coefficient of the quantum Fisher information matrix is bounded by $n_{\rm HS}\le \min\{p,k(k+3)/2\}$, which corresponds to the maximum number of independent combinations of parameters that can be estimated with Heisenberg-scaling sensitivity. The bound separates into two geometrically distinct contributions. The covariance contribution of the quantum Fisher information, which describes squeezing-enhanced fluctuations, provides at most $k(k+1)/2$ parameter combinations estimable at Heisenberg-scaling sensitivity, while the first-moment contribution provides at most $k$ additional independent parameter combinations with Heisenberg-scaling sensitivity. We identify the conditions for saturating these bounds and construct a passive family of interferometers that saturates these bounds.
