量子光力学中条件协方差的无偏估计
Unbiased Estimation of Conditional Covariance for Quantum Optomechanics
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中文总结 AI 辅助
研究量子光力学中条件协方差的无偏估计问题，通过从因果、追溯和平滑轨迹推导线性高斯估计器，解决传统方法有偏差的问题，为无偏测试宏观纠缠铺平道路，适用于多种规模的测试质量。
中文摘要 AI 辅助
连续测量可使宏观机械振子处于条件量子态，但其协方差难以验证。传统追溯估计器假定前后协方差对称且可能有偏差，因为反馈阻尼等物理动力学降低了从未来记录对状态的可观测性。本文从因果、追溯和平滑轨迹推导出精确的线性高斯估计器。对于毫克级镜子，它与基于独立固定参数的里卡蒂预测一致，而传统估计在协方差空间度量中存在大偏差，\(d_M \sim 5\)。该方法为在校准线性高斯模型中无偏测试宏观纠缠铺平道路，适用于桌面镜子及引力波千克级测试质量。
英文摘要
Continuous measurements can prepare macroscopic mechanical oscillators in conditional quantum states, but their covariance is difficult to verify. The conventional retrodictive estimator assumes a forward--backward covariance symmetry and can be biased, because physical dynamics such as feedback damping reduces the observability of the state from future records. Here, we derive an exact linear-Gaussian estimator from causal, retrodictive, and smoothed trajectories. For a milligram-scale mirror, it agrees with a Riccati prediction based on parameters fixed independently, while the conventional estimate exhibits a covariance-space bias of $d_M\simeq3.5$. Our method paves the way toward unbiased testing of macroscopic entanglement within a calibrated linear-Gaussian model, applicable to both tabletop mirrors and kg-scale gravitational-wave test masses.
