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We discuss a non-linear stochastic master equation that governs thetime-evolution of the estimated quantum state. Its differential evolutioncorresponds to the infinitesimal updates that depend on the time-continuousmeasurement of the true quantum state. The new stochastic master equationcouples to the two standard stochastic differential equations oftime-continuous quantum measurement. For the first time, we can prove that thecalculated estimate almost always converges to the true state, also atlow-efficiency measurements. We show that our single-state theory can beadapted to weak continuous ensemble measurements as well.Comment: 5 pages, RevTeX4. In version v2 some minor revisions and  clarifications have been incorporated. Moreover, a new reference has been  included. Accepted for publication in Journal of Physics A: Mathematical and  Genera

Coupled Ito equations of continuous quantum state measurement and estimation