Tracking Quantum Dynamics in an Optical Cavity for Recovering Purity and Squeezing via Quantum State Smoothing

Abstract: Tracking the dynamics of a quantum system is conventionally achieved by monitoring the system continuously in time and filtering the information contained in measurement records via the causal quantum trajectory approach. However, in practical scenarios there is often loss of information to the environment, leading to filtered states that are impure because of decoherence. If real-time tracking is not required, the lost information can be maximally extracted via acausal quantum state smoothing, which has been theoretically proven to better restore the system's coherence (purity) than causal filtering. Interestingly, quantum state smoothing requires assumptions of how any lost quantum information (unobserved by the experimenter) was turned into classical information by the environment. In this work, we experimentally demonstrate smoothing scenarios, using an optical parametric oscillator and introducing observed' andunobserved' channels by splitting the output beam into two independent homodyne detectors. We achieve improvement in state purification of 10.3% +/- 1.6%, squeezing restoration of 7.6% +/- 2.6%, and show that smoothed states are better estimates of hidden true states than those from conventional filtering. The estimation techniques used in this paper are promising for many applications in quantum information that incorporate post-processing.