Unbiased Estimation of Conditional Covariance for Quantum Optomechanics

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.

arXiv:2607.06431 [quant-ph]

(or arXiv:2607.06431v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.06431 Focus to learn more arXiv-issued DOI via DataCite

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