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arXiv · 2607.06431

Unbiased Estimation of Conditional Covariance for Quantum Optomechanics

Katsuta Sakai·Nobuyuki Matsumoto
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Abstract

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.

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Katsuta Sakai, Nobuyuki Matsumoto. 2026-07-07. Unbiased Estimation of Conditional Covariance for Quantum Optomechanics. https://arxiv.org/abs/2607.06431

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