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We investigate the estimation technique called quantum state smoothingintroduced by Guevara and Wiseman [Phys.~Rev.~Lett.~{\bf 115}, 180407 (2015)],which offers a valid quantum state estimate for a partially monitored system,conditioned on the observed record both prior and posterior to an estimationtime. Partial monitoring by an observer implies that there may exist recordsunobserved by that observer. It was shown that, given only the observed record,the observer can better estimate the underlying true quantum states, byinferring the unobserved record and using quantum state smoothing, rather thanthe usual quantum filtering approach. However, the improvement in estimationfidelity, originally examined for a resonantly driven qubit coupled to twovacuum baths, was also shown to vary depending on the types of detection usedfor the qubit's fluorescence. In this work, we analyse this variation in asystematic way for the first time. We first define smoothing power using anaverage purity recovery and a relative average purity recovery, of smoothingover filtering. Then, we explore the power for various combinations offluorescence detection for both observed and unobserved channels. We nextpropose a method to explain the variation of the smoothing power, based onmulti-time correlation strength between fluorescence detection records. Themethod gives a prediction of smoothing power for different combinations, whichis remarkably successful in comparison with numerically simulated qubittrajectories.

Quantum state smoothing: Why the types of observed and unobserved measurements matter