A smoother quantum measurement

Jay Lawrence

Jia Kong, Yaping Feng, Yihan Wang +2 more

Spin estimation plays a crucial role in quantum metrology, particularly in systems like atomic magnetometers where atomic spin ensembles transduce magnetic-field information into measurable optical signals. However, precise spin estimation remains challenging, especially in weak polarization schemes where signals are often obscured by both classical and quantum noise. Conventional fitting methods for spin signal and variance estimation are computationally intensive, lack real-time capabilities, and exhibit sensitivity to stochastic fluctuations and data-acquisition parameters. To address these challenges, we propose and demonstrate the implementation of a Kalman filter (KF) combined with a Rauch-Tung-Striebel (RTS) smoother for enhanced spin estimation across various polarization conditions. Our comprehensive analysis of spin conditional variance estimation reveals that the KF method achieves a remarkable 4.92-dB noise suppression compared to conventional fitting methods, while the RTS smoother provides further enhancement with 6.94-dB suppression that enables quantum noise squeezing observation. These findings offer new tools for quantum noise analysis and signal recovery, offering significant potential for advancing the performance of quantum-enhanced sensors and other precision measurement technologies.

W. E. Lawrence

Kentaro Ohki

In this paper, we develop a quantum smoothing theory to the class of open quantum systems driven by quantum jump-diffusion processes. A quantum smoothing theory, which is derived in a different senses by different researchers, has been applied for diffusive quantum Markovian systems, however, they only deal with quantum Wiener noises. We show how to derive the quantum smoother for quantum dynamical systems driven by quantum jump-diffusion noises.

Daniel F. Walls, Gerard J Milburn

Shibdas Roy, Obaid Ur Rehman, Ian R. Petersen +1 more

Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The estimation process is, however, desired to be made robust to uncertainties in the underlying parameters. Here, homodyne phase estimation of coherent and squeezed states of light, evolving continuously under the influence of a second-order resonant noise process, are made robust to parameter uncertainties using a robust fixed-interval smoother, designed for uncertain systems satisfying a certain integral quadratic constraint. We observe that such a robust smoother provides improved worst-case performance over the optimal smoother and also performs better than a robust filter for the uncertain system.