Unbiased Estimation of Conditional Covariance for Quantum Optomechanics

• URL: http://arxiv.org/abs/2607.06431v1
• Date: Tue, 07 Jul 2026 15:59:37 GMT
• Title: Unbiased Estimation of Conditional Covariance for Quantum Optomechanics
• Abstract summary: We derive an exact linear-Gaussian estimator from causal, retrodictive, and smoothed trajectories.<n>Our method paves the way toward unbiased testing of macroscopic entanglement within a calibrated linear-Gaussian model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 large bias in the covariance-space metric, $d_M \sim 5$. Our method paves the way toward unbiased testing of macroscopic entanglement within a calibrated linear-Gaussian model, which will be applicable to tabletop mirrors as well as gravitational-wave kg-scale test masses.

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