发表机构
School of Instrumentation and Optoelectronic Engineering, Beihang University（北京航空航天大学仪器科学与光电工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明高斯测量（如贝尔零差）可打破量子Fisher信息可加性，使两个独立模式联合测量优于分开测量，增益上限为17.157%，并在特定条件下可达12.699%。
AI 中文摘要
量子Fisher信息在独立探针上是可加的，因此单个参数最好逐个探针测量。我们证明高斯测量，即光学和微波实验中的线性光学与零差探测，打破了这一规则：两个独立模式一起测量效果更好。不确定性原理给线性探测器留下了一半相空间，而对于两个模式，这一半的选择是一种资源。贝尔零差，即一个平衡分束器后接两个零差探测器，在模式在正交宽度以及宽度对参数的响应方式上不同时，优于最佳的分开读出。外差探测在分束器上分裂一个模式以读取两个正交分量，并为空端口支付一个单位的真空噪声。贝尔零差用第二个模式填充该端口，因此噪声转化为信号。我们证明对于由宽度携带的每个参数，增益保持在$(\sqrt2-1)^2=17.157\\%$以下。对于单一温度下的热模式，即典型情况，曾猜想增益不可能存在。我们证明任何频率差异都会打开一个温度窗口，并且增益在频率比$3.318$处达到峰值$12.699\\%$，此时贝尔零差是最优的高斯测量。标准硬件可实现该增益：两个耦合谐振器配两个零差探测器，或一个相位保持放大器，其闲频带由同一热源馈入。
英文摘要
Quantum Fisher information adds over independent probes, so a single parameter is best measured probe by probe. We show that Gaussian measurements, the linear optics and homodyne detection of optical and microwave experiments, break this rule: two independent modes are better measured together. The uncertainty principle leaves a linear detector half of phase space, and for two modes the choice of half is a resource. Bell homodyne, a balanced beam splitter followed by two homodyne detectors, beats the best separate readout when the modes differ in quadrature width and in how the width responds to the parameter. Heterodyne detection splits a mode on a beam splitter to read both quadratures and pays one unit of vacuum noise for the empty port. Bell homodyne fills that port with the second mode, so the noise turns into signal. We prove that the gain stays below $(\sqrt2-1)^2=17.157\%$ for every parameter carried by widths. For thermal modes at one temperature, the canonical case, a gain was conjectured impossible. We prove that any frequency difference opens a temperature window and that the gain peaks at $12.699\%$ at frequency ratio $3.318$, where Bell homodyne is the optimal Gaussian measurement. Standard hardware reaches the gain: two coupled resonators with two homodyne detectors, or a phase-preserving amplifier whose idler band is fed by the same thermal source.
Comments32 pages, 10 figures
